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  • 251.
    Karim, Ehsanul
    et al.
    Blekinge Institute of Technology, School of Engineering.
    Madani, Sri Phani Venkata Siva Krishna
    Blekinge Institute of Technology, School of Engineering.
    Yun, Feng
    Blekinge Institute of Technology, School of Engineering.
    Fuzzy Clustering Analysis2010Independent thesis Advanced level (degree of Master (Two Years))Student thesis
    Abstract [en]

    The Objective of this thesis is to talk about the usage of Fuzzy Logic in pattern recognition. There are different fuzzy approaches to recognize the pattern and the structure in data. The fuzzy approach that we choose to process the data is completely depends on the type of data. Pattern reorganization as we know involves various mathematical transforms so as to render the pattern or structure with the desired properties such as the identification of a probabilistic model which provides the explaination of the process generating the data clarity seen and so on and so forth. With this basic school of thought we plunge into the world of Fuzzy Logic for the process of pattern recognition. Fuzzy Logic like any other mathematical field has its own set of principles, types, representations, usage so on and so forth. Hence our job primarily would focus to venture the ways in which Fuzzy Logic is applied to pattern recognition and knowledge of the results. That is what will be said in topics to follow. Pattern recognition is the collection of all approaches that understand, represent and process the data as segments and features by using fuzzy sets. The representation and processing depend on the selected fuzzy technique and on the problem to be solved. In the broadest sense, pattern recognition is any form of information processing for which both the input and output are different kind of data, medical records, aerial photos, market trends, library catalogs, galactic positions, fingerprints, psychological profiles, cash flows, chemical constituents, demographic features, stock options, military decisions.. Most pattern recognition techniques involve treating the data as a variable and applying standard processing techniques to it.

  • 252.
    Karlsson, Tim
    Blekinge Institute of Technology, School of Computing.
    Implementing Cauchy Reed-Solomon Utilizing OpenCL2013Student thesis
    Abstract [en]

    In this paper the performance of executing Cauchy Reed-Solomon (CRS) coding on the GPU is evaluated and compared with execution on the CPU. Three different prototypes are developed. One is sequential and developed in C++, the other two are developed utilizing C++ and OpenCL. The measurements are done by comparing the execution time of different data block sizes ranging from 16KB up to 256MB with two different encoding ratios, 9/12 and 10/16. The measurements are done on an Intel CPU with 4 cores with an integrated graphics card and an AMD graphics card. The OpenCL prototypes are executed with three different targets, the CPU, the integrated graphics card and the AMD graphics card. The sequential prototype is executed on the same CPU, but on a single core. The results from the measurements show that the GPU is faster than the CPU on larger data sizes. The highest measured throughput is achieved with the multithreaded CPU prototypes (OpenCL executed on the CPU) for sizes around 1MB.

  • 253.
    Khaliq, Abdul
    et al.
    Blekinge Institute of Technology, School of Engineering.
    Ahmad, Amais
    Blekinge Institute of Technology, School of Engineering.
    Fuzzy Logic and Approximate Reasoning2010Independent thesis Advanced level (degree of Master (Two Years))Student thesis
    Abstract [en]

    Two of the most exemplary capabilities of the human mind are the capability of using perceptions (human knowledge) in purposeful ways and the capability of approximating perceptions by statements in natural language. Understanding these capabilities and emulating them by linguistic approximation is the crux of our thesis. There has been a rapid growth in the number and variety of applications of fuzzy logic. In a narrow sense, fuzzy logic is a logical system which is an extension of multivalued logic and is intended to serve as logic of approximate reasoning. But in a wider sense, fuzzy logic is more or less synonymous with the theory of fuzzy sets. In classical logic the propositional value of a statement is either true (1) or false (0) but in lukasiewicz logic we gave value as a truthfulness to a certain proposition between [0, 1]. As a generalization of many valued logic, fuzzy logic was established in order to deal with those fuzzy propositions and to underlie approximate reasoning. We have calculated the fuzzy truth values and compare the results of different operations (conjunction, disjunction etc) with the approach to Baldwin's (1979) and with the help of modus ponens law. There are many chemical reactions that are very sensitive and a little change in temperature and particle size can create serious problems. We have developed the idea of approximate reasoning and fuzzy logic to find the approximate value of reaction rate with the given conditions by means of the extended modus ponens law. The methodology is very simple and can be applied to several other chemical reactions in the similar way by connecting AND and OR operations. The result Q' can be found by the fuzzy relation equation Q' = P' o R where ``o" is the max-min composition of P' and R operation. Result Q' for the certain situation is in the form of fuzzy set, in which we choose the value with maximum membership degree.

  • 254.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Self-Adjointness and Quasi-Self-Adjointness of the Magma Equation2008Conference paper (Refereed)
    Abstract [en]

    A recent theorem on nonlocal conservation laws is applied to a magma equation modelling a melt migration through the Earth´s mantle. It is shown that the equation in question is quasi-self-adjoint. The self-adjoint equations are singled out. Nonlocal and local conservation densities are obtained using the symmetries of the magma equation.

  • 255.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Symmetries and conservation laws2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.

  • 256. Khamitova, Raisa
    Symmetries and Nonlocal Conservation Laws of the General Magma Equation2009In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 14, no 11, p. 3754-3769Article in journal (Refereed)
    Abstract [en]

    In this paper the general magma equation modelling a melt flow in the Earth's mantle is discussed. Applying the new theorem on nonlocal conservation laws [Ibragimov NH. A new conservation theorem. J Math Anal Appl 2007;333(1):311-28] and using the symmetries of the model equation nonlocal conservation laws are computed. In accordance with Ibragimov [Ibragimov NH. Quasi-self-adjoint differential equations. Preprint in Archives of ALGA, vol. 4, BTH, Karlskrona, Sweden: Alga Publications; 2007. p. 55-60, ISSN: 1652-4934] it is shown that the general magma equation is quasi-self-adjoint for arbitrary m and n and self-adjoint for n = -m. These important properties are used for deriving local conservation laws. © 2008 Elsevier B.V. All rights reserved.

  • 257. Khamuknin, Alexander
    et al.
    Bertoni, Marco
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Eres, Hakki Murat
    Avoiding Resonant Frequencies in a Pipeline Application by Utilising the Concept Design Analysis Method2015Conference paper (Refereed)
    Abstract [en]

    Avoiding disasters due to the problems stemming from resonance is a major concern in any construction project. This becomes particularly important for oil and gas pipeline systems as some damages may lead to leakage of flammable fluids, explosions, fires, destruction and loss of life. The proximity to the natural frequencies of forced frequencies (frequency ratio) normally leads to intolerant resonant vibrations and catastrophic failures. A relevant case study on a partial pipeline design with an unacceptable level of frequency ratio is presented. In order to assess the overall design merit of the case study, the Concept Design Analysis (CODA) method is utilised to map captured Customer Needs (CNs) into Engineering Characteristics (ECs). As the frequency ratio is an important EC of the whole system, the improved CODA method for the pipeline design introduces an avoidance type merit function that allows excluding a range of relevant ECs. This improved CODA method is demonstrated in a model whereby certain frequency ratios are successfully avoided in the final design.

  • 258.
    Khan, Fahim
    et al.
    Blekinge Institute of Technology, Faculty of Computing, Department of Communication Systems.
    Mazarati, Pierre Celestin
    Blekinge Institute of Technology, Faculty of Computing, Department of Communication Systems.
    Khan, Nasir
    Blekinge Institute of Technology, Faculty of Computing, Department of Communication Systems.
    Effect of Primary Network on Performance of Spectrum Sharing System over Nakagami-m Fading Channel2013Independent thesis Advanced level (degree of Master (Two Years))Student thesis
    Abstract [en]

    During the last few years, we have witnessed that radio spectrum is becoming a valuable and scarce resource due to the increasing demand of multimedia services. However, recent research has shown that most of the available radio spectrum is not used effectively and is wasted. So, to utilize the radio spectrum effectively, a new technology has been introduced known as “Cognitive Radio”. In cognitive radio, a secondary user (SU) uses the vacant holes in licensed spectrum when it is not occupied by a primary user (PU) without causing interference to the PU transmission. Accessing vacant holes in the licensed user spectrum without causing interference to the PU is a complicated task. Therefore, alternative spectrum sharing techniques have gained popularity. Using these techniques, an SU can share the licensed spectrum with a PU at the same time without causing interference to the PU transmission. As a result, a secondary user should have an optimal power allocation policy in order to get a high transmission rate while still keeping the interference caused to the primary user below a threshold value. Under limited spectrum conditions, spectrum sharing relay networks have gained much popularity by providing reliability over direct transmission. In this thesis, we investigate an amplify-and-forward (AF) relay network performance in a spectrum sharing environment. Here, we consider the impact of the primary transmitter on the spectrum sharing system in the presence of a Nakagami-m fading channel, where the fading parameter m (m is an integer) can be used to deal with a variety of channel scenarios.

  • 259.
    Khan, Khalid
    Blekinge Institute of Technology, School of Computing.
    The Evaluation of Well-known Effort Estimation Models based on Predictive Accuracy Indicators2010Independent thesis Advanced level (degree of Master (Two Years))Student thesis
    Abstract [en]

    Accurate and reliable effort estimation is still one of the most challenging processes in software engineering. There have been numbers of attempts to develop cost estimation models. However, the evaluation of model accuracy and reliability of those models have gained interest in the last decade. A model can be finely tuned according to specific data, but the issue remains there is the selection of the most appropriate model. A model predictive accuracy is determined by the difference of the various accuracy measures. The one with minimum relative error is considered to be the best fit. The model predictive accuracy is needed to be statistically significant in order to be the best fit. This practice evolved into model evaluation. Models predictive accuracy indicators need to be statistically tested before taking a decision to use a model for estimation. The aim of this thesis is to statistically evaluate well known effort estimation models according to their predictive accuracy indicators using two new approaches; bootstrap confidence intervals and permutation tests. In this thesis, the significance of the difference between various accuracy indicators were empirically tested on the projects obtained from the International Software Benchmarking Standard Group (ISBSG) data set. We selected projects of Un-Adjusted Function Points (UFP) of quality A. Then, the techniques; Analysis Of Variance ANOVA and regression to form Least Square (LS) set and Estimation by Analogy (EbA) set were used. Step wise ANOVA was used to form parametric model. K-NN algorithm was employed in order to obtain analogue projects for effort estimation use in EbA. It was found that the estimation reliability increased with the pre-processing of the data statistically, moreover the significance of the accuracy indicators were not only tested statistically but also with the help of more complex inferential statistical methods. The decision of selecting non-parametric methodology (EbA) for generating project estimates in not by chance but statistically proved.

  • 260.
    khan, Maqsood Muhammad
    et al.
    Blekinge Institute of Technology, School of Computing.
    khan, Muhammad Saad
    Blekinge Institute of Technology, School of Computing.
    INVESTIGATION OF HANDOVERS IN 3G UMTS TRAFFIC CLASSES2010Independent thesis Advanced level (degree of Master (Two Years))Student thesis
    Abstract [en]

    The Universal Mobile Telecommunication systems are one of the emerging cellular phone technologies which are known as the 3G systems. It support the high speed data transfer, speech, web browsing, email, video telephony, multimedia and the audio streaming. These services are divided in to the classes depending upon the QoS requirements. With the development of these cellular networks, a major problem came up; it was the call handover from one cell to the other cell during an ongoing session without dropping the connection with the base station. A lot of techniques were developed and used to cope with this major issue. The user’s movement is a dynamic process considering its location. This means that the mobile users can change its way any time with any speed, so there should be a mechanism and a way that the network should be aware of this process. For this purpose different types of handovers techniques are used which include soft, hard and softer handovers. The thesis work is about the investigation of different handovers in the 3G UMTS network which is the vital issue to the network to maintain the user’s connection during in the ongoing session with the user’s movement. The investigation is based on the UMTS QoS traffic classes. For this purpose the soft and the hard handovers techniques are analyzed in different scenarios implemented in the OPNET Modeler. To know and understand about the handover process between the Node B and the user equipment different statistics are calculated.

  • 261.
    Khan, Mubbashar Altaf
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Telecommunication Systems.
    Ahmad, Sohaib
    Blekinge Institute of Technology, School of Engineering, Department of Telecommunication Systems.
    Decision Making Techniques for Cognitive Radios2008Independent thesis Advanced level (degree of Master (One Year))Student thesis
    Abstract [en]

    Spectrum scarcity is one of the biggest challenges that the modern world is facing. The efficient use of available licensed spectrum is becoming more and more critical with increasing demand and usage of the radio spectrum. Different researches show that the usage is not uniform throughout the licensed spectrum rather it is heavy in certain parts of the spectrum and has portions that are utilized inefficiently. Some researchers even claim that more than 70% of the licensed frequency band is not in use, most of the time. So, there is much room for work yet in the unutilized parts or the inefficiently utilized parts of the spectrum, to overcome the spectrum scarcity problem. Different researches are in progress and ways are being found to efficiently utilize the available licensed spectrum. One of the ways is the use of “Cognitive Radio”, according to this; the already licensed spectrum can be used more efficiently by introducing artificial intelligence, the decision-making to be specific, in the radio. This enables the radio to learn from its environment, considering certain parameters. Based on this knowledge the radio can actively exploit the possible empty frequencies in the licensed band of the spectrum that can then be assigned to other processes in such a way that they don’t cause any interference to the frequency band that is already in use. This makes the efficient usage of the available licensed spectrum possible. The users that are allocated the licensed frequency bands of the spectrum are the primary users and the users that are allocated the empty frequencies within the licensed frequency band, according to their requested QoS specifications, are known as the secondary users or the cognitive users. They are called as the secondary users as they utilize the unused spectrum resources only, on non-interfering basis, with the primary users. This thesis will focus on the implementation of different spectrum allocation techniques for these secondary users, based on Genetic Algorithms and an evaluation of the performance of these techniques using Matlab coding. This research will focus on the decision-making process mainly, with an assumption that the radio environment has already been sensed and the QoS requirements for the application have been specified either by the sensed radio environment or by the secondary user itself.

  • 262.
    Khan, Yawar Saeed
    Blekinge Institute of Technology, School of Management.
    STRATEGIES OF HIGHER EDUCATION IN PAKISTAN BASED ON ENDOGENOUS GROWTH2009Independent thesis Advanced level (degree of Master (One Year))Student thesis
    Abstract [en]

    This paper investigates the possible opportunities for Higher Education in Pakistan towards gaining a competitive advantage in the international community, the link between Human capital development and GDP growth in Pakistan and finally compares the HE policies in Pakistan and the EU. We look at empirical evidence and statistical data to investigate how endogenous growth affects the GDP per capita with the case study of Pakistan. The empirical studies show that employing human capital variable in the endogenous production function does not have favorable results on the economic growth output. This leads us to believe that the measuring criterion for Human Capital has to be re-evaluated as there are several factors that affect the educational systems in different parts of the world See Barro (2001), Qaisar (2007) and De la Fuente and Doménech (2002). Hence the definition of Human Capital can vary from region to region in order to get accurate results from the endogenous production function. We performed Pearsons Correlation function on 7 years data of GDP growth, GDP per capita GDP PPP compared with various variables including higher education enrollment rates and labor force in Pakistan. The results show little or no correlation is all experiments which further validate empirical research by Qaisar Abbas. These results are confirming the theory that the Higher Education growth cannot be simply measured in terms of enrollment rates and other variables must be included in the equation. These variables can vary from country to country and a multi ethnic country like Pakistan, measuring these variables is a complex task due to heterogeneous environments. Empirical evidence states that there is a link between human capital and spatial heterogeneity in Pakistan. Unequal opportunities are defeating the advantages of existing supplies of Human Capital. Minimization of educational inequalities enables the poor to receive more benefits of economic growth and that in turn allows the increase in growth rates for the country. A public survey was conducted to investigate general public’s awareness and attitude towards acceptance of Higher Education as a key towards quality of Life and opportunities in Higher Education for a common man in Pakistan. Overall 280 respondents from across Pakistan were engaged. Public survey results show that there is a strong sense of awareness in the general public about higher education being the Key for economic revival in Pakistan. Despite being motivated for educational growth there are various elements that are unattractive for public to pursue a higher degree in Pakistan. We take of look at the survey response towards acceptance of a Pakistani degree against a foreign degree and find that education institutions of Pakistan are majorly unattractive for our prospective future Human Capital supplies. In light of these findings and research studies, we identify a few areas in which the education institutes can impact their internal and external environments to meet the challenges posed in front of them. In the second leg of this dissertation, we perform an analytical review of the background and present status of EU Higher Education policies in contrast to Pakistani Higher Education policies. This dissertation reveals a sharp contrast between the history, plans and implementation of HE Policies in the EU and Pakistan. In the EU, dynamic policy making in the light of the intergovernmental Bologna Process and the Lisbon Strategy is evident how HE has evolved in the EU and provided a roadmap to Lisbon/Bologna declarations [2]. In Pakistan, we can only witness some enthusiastic plans, but lack of implementation force backed with unrealistic economic forecasts which ultimately played a major role in policy failure [3][4]. A detailed analysis and comparison is performed between EU and Pakistan in order to identify benchmarks for Pakistan. We find there are a need of exchange programs at all levels in Pakistan in order to establish a knowledge based community which in turn can be expanded in collaboration wi th other communities and possibly with EU in the form of Bologna process. In the end of the dissertation we conclude that the existing theory of human capital growth has strong relevance in the field of higher education as indicated by our experiments and empirical evidence from Qaisar, Jamal and Hasan. The survey results support the fact that there economic growth is deeply severed due to insufficient supplies of Human capital, the studies and survey results support that fact that un-equal opportunities and lack of financial aid for students is defeating our cause to utilize our demographic dividend or working age group of Human Capital before we enter 2050 and become one of biggest populated nations in the world. Empirical studies tell us that at least 40% of development in East Asian countries can be attributed towards their Human Capital (Demographic dividend)[1]. Pakistan has to capitalize on her Human Capital stock in order to translate this opportunity of a demographic dividend into global economic power. We briefly look into the spatial heterogeneity aspect of human capital growth and knowledge spillovers as possible solution to minimize the silos culture within regions. This dissertation is a non-technical review of Endogenous Growth theories, its application across the countries and in Pakistan. We conclude this dissertation by suggesting some changes in the internal and external environments of higher education institutes and higher education policy re-evaluation in Pakistan. We have identified certain areas of improvement which the Government of Pakistan should consider.

  • 263.
    Klonowska, Kamilla
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Systems and Software Engineering.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Lundberg, Lars
    Blekinge Institute of Technology, School of Engineering, Department of Systems and Software Engineering.
    Svahnberg, Charlie
    Blekinge Institute of Technology, School of Engineering, Department of Systems and Software Engineering.
    Optimal recovery schemes in fault tolerant distributed computing2005In: Acta Informatica, ISSN 0001-5903, E-ISSN 1432-0525, Vol. 41, no 6, p. 341-365Article in journal (Refereed)
    Abstract [en]

    Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all n computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down, the load on these computers must be redistributed to other computers in the system. The redistribution is determined by the recovery scheme. The recovery scheme is governed by a sequence of integers modulo n. Each sequence guarantees minimal load on the computer that has maximal load even when the most unfavorable combinations of computers go down. We calculate the best possible such recovery schemes for any number of crashed computers by an exhaustive search, where brute force testing is avoided by a mathematical reformulation of the problem and a branch-and-bound algorithm. The search nevertheless has a high complexity. Optimal sequences, and thus a corresponding optimal bound, are presented for a maximum of twenty one computers in the distributed system or cluster.

  • 264. Klonowska, Kamilla
    et al.
    Lundberg, Lars
    Lennerstad, Håkan
    Broberg, Magnus
    Comparing the optimal performance of parallel architectures2004In: Computer journal, ISSN 0010-4620, E-ISSN 1460-2067, Vol. 47, no 5, p. 527-544Article in journal (Refereed)
    Abstract [en]

    Consider a parallel program with n processes and a synchronization granularity z. Consider also two parallel architectures: an SMP with q processors and run-time reallocation of processes to processors, and a distributed system (or cluster) with k processors and no run-time reallocation. There is an inter-processor communication delay of t time units for the system with no run-time reallocation. In this paper we define a function H(n,k,q,t,z) such that the minimum completion time for all programs with n processes and a granularity z is at most H(n,k,q,t,z) times longer using the system with no reallocation and k processors compared to using the system with q processors and run-time reallocation. We assume optimal allocation and scheduling of processes to processors. The function H(n,k,q,t,z)is optimal in the sense that there is at least one program, with n processes and a granularity z, such that the ratio is exactly H(n,k,q,t,z). We also validate our results using measurements on distributed and multiprocessor Sun/Solaris environments. The function H(n,k,q,t,z) provides important insights regarding the performance implications of the fundamental design decision of whether to allow run-time reallocation of processes or not. These insights can be used when doing the proper cost/benefit trade-offs when designing parallel execution platforms.

  • 265. Klonowska, Kamilla
    et al.
    Lundberg, Lars
    Lennerstad, Håkan
    Svahnberg, Charlie
    Extended Golomb Rulers as the New Recovery Schemes in Distributed Dependable Computing2005Conference paper (Refereed)
    Abstract [en]

    Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down the load on these computers must be redistributed to other computers in the cluster. The redistribution is determined by the recovery scheme. The recovery scheme should keep the load as evenly distributed as possible even when the most unfavorable combinations of computers break down, i.e. we want to optimize the worst-case behavior. We have previously defined recovery schemes that are optimal for some limited cases. In this paper we find a new recovery schemes that are based on so called Golomb rulers. They are optimal for a much larger number of cases than the previous results.

  • 266. Kovalev, Guest editors: N.H. Ibragimov and V.F.
    Special issue: Group analysis of nonlinear wave problems2004Other (Other academic)
    Abstract [en]

    "Communications in Nonlinear Science and Numerical Simulation'' is given entirely to appreciation of applications of Lie groups to nonlinear problems in acoustics, engineering, biomedicine, etc. The selection of papers covers the following topics: a) group classification of differential equations and optimal systems of invariant and partially invariant solutions including classification of differential equations according to their symmetries; b) equivalence groups and invariants of families of differential equations; c) symmetries of delay equations; d) symmetries of stochastic differential equations; e) application to nonlinear physics and biomathematics. We hope that this special issue highlights the recent major developments in this fascinating field of mathematics and mathematical modelling.

  • 267. Krasemann, Johanna Törnquist
    Design of an Effective Algorithm for Fast Response to the Rescheduling of Railway Traffic During Disturbances2009Conference paper (Refereed)
    Abstract [en]

    The increased occurrence of railway traffic disturbances shows that effective re-scheduling is important. In previous research we have designed an optimization-based approach which seems promising. However, for some scenarios it is difficult to find good solutions within seconds. Therefore, we have developed a greedy algorithm which effectively delivers good solutions within the permitted time. To quickly retrieve a feasible solution the algorithm performs a depth-first search using an evaluation function to prioritise when conflicts arise and then branches according to a set of criteria.

  • 268. Krasemann, Johanna Törnquist
    Greedy algorithm for railway traffic re-scheduling during disturbances: a Swedish case2010In: IET Intelligent Transport Systems, ISSN 1751-956X, E-ISSN 1751-9578, Vol. 4, no 4Article in journal (Refereed)
    Abstract [en]

    The positive trend of increased use of railway transportation in Europe has resulted in an increased sensitivity to and occurrence of traffic disturbances. In addition to the need for extensions of the infrastructure, the need to effectively limit and predict the effects of disturbances becomes apparent. The kernel of the disturbance management problem is to revise the original timetable in line with the new conditions and decide where, when and how trains should overtake or meet to minimise the negative effect of the disturbance. In previous research, the author has designed optimisation-based approach for rescheduling, which seems promising, but for some scenarios it is difficult to find good solutions within seconds. Also, more detailed constraints will have to be included, which makes the problem even more complex and difficult to solve. Therefore the author developed a greedy algorithm that effectively delivers good solutions within the permitted time. To quickly retrieve a feasible solution, the algorithm performs a depth-first search using an evaluation function to prioritise when conflicts arise and then branches according to a set of criteria. A performance analysis of the algorithm was carried out using simulated experiments showing its strengths and weaknesses.

  • 269. Krasemann, Johanna Törnquist
    Pros and cons of increased complexity in re-scheduling strategies for railway traffic disturbances: A Swedish case2009Conference paper (Refereed)
    Abstract [en]

    The positive trend of increased use of both railway passenger and freight transportation in Europe has resulted in an increased sensitivity to and occurrence of traffic disturbances. In addition to the need for extensions of the infrastructure, the need to effectively limit and predict the effects of disturbances becomes apparent. The abilities to maximise the use of available infrastructure such as sidings and platforms as well as the tracks in both directions is therefore critical. The kernel of the disturbance management problem is to revise the original timetable in line with the new conditions and decide where, when and how trains should overtake or meet to minimise the negative effect of the disturbance. There exist both sophisticated and simple models and methods which have different strengths and weaknesses. This paper presents results from a Swedish research project and investigates the pros and cons of different re-scheduling models and methods.

  • 270. Kurach, Damian
    et al.
    Rutkowska, Danuta
    Rakus-Andersson, Elisabeth
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Face Classification Based on Linguistic Description of Facial Features2014Conference paper (Refereed)
    Abstract [en]

    This paper presents an Artificial Intelligence approach towards classification of persons based on a verbal description of their facial features. Face features are extracted by use of an existing detection techniques, such as measurements of horizontal and vertical size of the facial elements like nose, eyes, etc. This approach allows to create fuzzy sets representing selected facial features. What is important, linguistic variables corresponding to the fuzzy sets conform the terminology applied by law enforcement to create an eyewitness verbal description. Then, fuzzy IF-THEN rules are employed for classification both the facial composites (sketches) and usual images from face databases. With regard to this concept, satisfactory results have been obtained and presented.

  • 271. Laksman, Efraim
    Bounds on the Performance of PSK Block Codes2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In wireless communication, the minimum Euclidean distance between codewords is a major factor for the ability to correct errors in messages, and it is of interest to maximize the minimum Euclidean distance. The thesis improves previously established general upper bounds on minimum Euclidean distance of phase shift keying block codes. There are no requirements on structure of codes, as the bound depends only on alphabet size, word length and code size. Prior to this thesis, bounds found by use of a method of Elias, had been improved by generalization of Elias' method. The method used here is an attempt to optimize that generalization.

  • 272.
    Laksman, Efraim
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Combinatorial Optimization: Three Applications2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Combinatorial optimization is a diverse area of mathematics. It concerns optimization on feasible regions defined by discrete sets, graphs, hypergraphs, matroids, etc. . . which all have a large number of applications. They occur in virtually all domains of human activity since humans always want to do things easier, faster, consume less resources, etc. . . This thesis concerns three applied problems within combinatorial optimization. The first paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase-shift keying (PSK) block codes, that are explicit in the parameters alphabet size, block length and code size. There is a strong connection between high minimum Euclidean distance and good error-correcting capabilities. The bounds are generalized in several respects, such as from codes on symmetric PSK to codes on asymmetric PSK. They are also generalized to other types of noise than Gaussian, allowing more efficient block codes when noise is non-Gaussian. We provide examples of codes on asymmetric PSK that have higher minimum Euclidean distance than any comparable codes on symmetric PSK.Several classes of codes are shown to be optimal among codes on symmetric PSK since their Euclidean distance coincides with the bound. The second paper considers a parallel computer system with m identical computers,where we study optimal performance precaution for one possible computer crash. We anticipate that some computer may crash, and restrict the cost in such a situation. How costly is such a precaution when no crash occurs? We set a restriction that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use an optimal allocation with m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time defines a function f(r,m). In the paper we establish upper and lower bounds of the worst-case cost function f(r,m) and characterize worst-case programs. The third paper considers the problem of Map Matching (MM), i.e. matching time and location measurements of a vehicle to a route in a road network. The paper presents a probabilistic algorithm for MM based on a second order hidden Markov model (HMM), as opposed to first order HMMs which are usually used. This allows a more detailed analysis of the data while preserving algorithmic complexity O(n). Both measurement densities and transition probabilities are determined with respect to Kolmogorov's third axiom, which in this context implies that the probabilities are additive over a partition of a road segment.

  • 273.
    Laksman, Efraim
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Lundberg, Lars
    Blekinge Institute of Technology, School of Computing.
    Optimal computer crash performance precaution2012In: Discrete Mathematics and Theoretical Computer Science, ISSN 1462-7264, Vol. 14, no 1, p. 55-68Article in journal (Refereed)
    Abstract [en]

    For a parallel computer system withmidentical computers, we study optimal performance precaution for one possible computer crash. We want to calculate the cost of crash precaution in the case of no crash. We thus define a tolerance level r meaning that we only tolerate that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use optimal allocation on m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then, what is the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time of the same parallel program? We denote the maximal ratio of completion times f(r, m) - i.e., the ratio for worst-case programs. In the paper we establish upper and lower bounds of the worst-case cost function f(r, m) and characterize worst-case programs.

  • 274. Laksman, Efraim
    et al.
    Lennerstad, Håkan
    Nilsson, Magnus
    Bounding the minimal Euclidean distance for any PSK block codes of alphabet size 82009Conference paper (Refereed)
    Abstract [en]

    We consider a bound for the minimal Euclidean distance of any PSK block code with eight symbols. The main result was established in [6] - here we prove that the bound is in fact stronger than was proven there. The bound is deduced by generalizing Elias' method of a critical sphere. It is not asympthotic, as previous Elias' sphere bounds, but valid for any specific word length and code size. Many known codes fulfil the bound with equality, proving the sharpness of the bound for these parameter values as well as the optimality of these codes.

  • 275.
    Laksman, Efraim
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Lennerstad, Håkan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Nilsson, Magnus
    Generalized upper bounds on the minimum distance of PSK block codes2015In: IMA Journal of Mathematical Control and Information, ISSN 0265-0754, E-ISSN 1471-6887, Vol. 32, no 2, p. 305-327Article, review/survey (Refereed)
    Abstract [en]

    This paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase shift keying (PSK) block codes, that are explicit in three parameters: alphabet size, block length and code size. The bounds are primarily generalized from codes over symmetric PSK to codes over asymmetric PSK and also to general alphabet size. Furthermore, block codes are optimized in the presence of other types of noise than Gaussian, which induces also non-Euclidean distance measures. In some instances, codes over asymmetric PSK prove to give higher Euclidean distance than any code over symmetric PSK with the same parameters. We also provide certain classes of codes that are optimal among codes over symmetric PSK.

  • 276. Laksman, Efraim
    et al.
    Lennerstad, Håkan
    Nilsson, Magnus
    Improving bounds on the minimum Euclidean distance for block codes by inner distance measure optimization2010In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 310, no 22 Special issue SI, p. 3267-3275Article in journal (Refereed)
    Abstract [en]

    The minimum Euclidean distance is a fundamental quantity for block coded phase shift keying (PSK). In this paper we improve the bounds for this quantity that are explicit functions of the alphabet size q, block length n and code size | C |. For q = 8, we improve previous results by introducing a general inner distance measure allowing different shapes of a neighborhood for a codeword. By optimizing the parameters of this inner distance measure, we find sharper bounds for the outer distance measure, which is Euclidean. The proof is built upon the Elias critical sphere argument, which localizes the optimization problem to one neighborhood. We remark that any code with q = 8 that fulfills the bound with equality is best possible in terms of the minimum Euclidean distance, for given parameters n and | C |. This is true for many multilevel codes.

  • 277. Laksman, Efraim
    et al.
    Lennerstad, Håkan
    Nilsson, Magnus
    Inner Distance Measure Bounds on the Minimal Euclidean Distance for Symmetric PSK Block Codes2009Conference paper (Refereed)
    Abstract [en]

    The minimum Euclidean distance is a fundamental quantity for block-coded PSK. In this paper improvements are made of bounds for this quantity that are explicit functions of the alphabet size q, block length n and code size |C|. Earlier work, where the restriction q=8 was used, is continued by a generalisation allowing any q. The bound generalizes Elias critical sphere argument, which localizes the optimization problem to one neighbourhood, by use of so called inner distance measure for defining the shape of a sphere. Remark that codes which fulfill the bound with equality exist, and are best possible in terms of minimum Euclidean distance, for given parameters q, n and |C|.

  • 278. Lennerstad, Håkan
    An evolutionary textbook evolving by student activity2007In: Journal of Online Mathematics and its Applications, ISSN 1935-6439 , Vol. 7, no JuneArticle in journal (Refereed)
    Abstract [en]

    Successful education requires that the teacher has two knowledge competencies. The teacher not only needs to be familiar with the subject knowledge, it is also essential that the teacher have a realistic, detailed and practical knowledge of the students' understanding of the subject. This second kind of knowledge concerns the students' typical understanding and misunderstanding of the subject, and ways to handle them. It also includes ways to communicate meaning and interest in the subject--not to idealized students, but to real students. This paper describes a Swedish project that opens a channel allowing a teacher to systematically develop this knowledge while helping students. Teacher-student dialogues are conducted through a web page. As a result of the underlying goal, the project also extends the students' role in their education to a more responsible one. The textbook author uses the students' opinions and work at the web page to improve the book for the benefit of future students. Thus, the textbook evolves to be better adapted to the environment for which it is intended: studies by students. We present empiric results for an undergraduate distance course in calculus with 20 students.

  • 279. Lennerstad, Håkan
    Commensurable and rational triangles2007Report (Other academic)
    Abstract [en]

    One may ask which property the equilateral, the right isosceles, the half equilateral, and the two golden triangles, with angles (π/5),((2π)/5),((2π)/5) and (π/5),(π/5),((3π)/5), have in common. One answer is that their angles are commensurable with each other -- such triangles are commensurable. We investigate properties of this class of triangles, which is a countable subset of the entire class of triangles -- we do not distinguish between similar triangles. It can naturally be endowed with a family structure by integer triples. The equilateral is the only member of the first generation, and the other triangles mentioned above populate the first generations. A formula for the number of non-similar triangles that can be formed by triples of corners in a regular n-polygon is calculated, which gives the number of commensurable triangles at each generation. Three "metatriangles" are described -- so called because each possible triangle is represented as a point in each of them. The set of right triangles form a height in one of the metatriangles. The eye is the point of a metatriangle in the same metatriangle. In the second part of this report, triangles are studied by side length. A rational triangle is a triangle where all sides and all heights are rational numbers. We show that the right rational triangles are the Pythagorean triangles, and each non-right rational triangle consists of two Pythagorean triangles. Almost all triangles are irrational. It turns out that no Pythagorean triangle is commensurable. We prove that the only triangle with commensurable angles and also commensurable sides is the equilateral triangle.

  • 280. Lennerstad, Håkan
    Envariabelanalys, idéer och kalkyler2005Book (Other academic)
  • 281.
    Lennerstad, Håkan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Local Linear Time Convergence of a Primal-Dual Energy Minimization Algorithm for Parallel Processing2014Conference paper (Refereed)
    Abstract [en]

    We consider energy minimization by speed-scaling of an open shop multiprocessor with n jobs and m machines. The paper studies the complexity of a primal-dual solution algorithm of [4], which was an open question in that paper.We prove that in a neighbourhood of the solution the complexity of the algorithm is O(mn log(1/ε) if n and m are not equal and ε is the roundoff error of the computer. The paper demonstrates how linearization can be used to investigate the complexity of an algorithm close to the optimum. An estimate of the size of the neighbourhood where the linearization error is smaller than the computer’s roundoff error is also given.

  • 282. Lennerstad, Håkan
    Logical graphs: how to map mathematics1996In: ZDM - Zentralblatt für Didaktik der Mathematik, ISSN 0044-4103, Vol. 27, no 3, p. 87-92Article in journal (Refereed)
    Abstract [en]

    A logical graph is a certain directed graph with which any mathematical theory or proof can be presented - its logic is formulated in graph form. Compared to the usual narrative description, the presentation usually gains in survey, clarity and precision. A logical graph formulation can be thought of as a detailed and complete map over the mathematical landscape. The main goal in the design of logical graphs is didactical: to improve the orientation in a mathematical proof or theory for a reader, and thus to improve the access of mathematics.

  • 283.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Matematikens dubbelnatur –undflyende innehåll,självtillräckligt språk2005In: Utbildning och Demokrati, ISSN 1102-6472, E-ISSN 2001-7316, Vol. 14, no 2, p. 27-55Article in journal (Refereed)
    Abstract [en]

    This article discusses the role in mathematics of its formal language, here called Mathematish. This language became significant when symbolic mathematics gradually replaced rhetoric mathematics. Mathematics gained in efficiency and calculation became dominant. It is claimed that this happened on the expense of mathematical interpretation, except for those who intuitively understand Mathematish. It is also claimed by linguistic arguments that the structure of a language isnaturally non-articulated for intuitive learners, often teachers, while teaching requires articulation. Languages are often excluding. Therelationship between content and language in mathematics is described from several viewpoints. Three distinct types of mathematical knowl-edge are suggested: 1. How to successfully use Mathematish rules, 2. Mathematish rules (computer programmable grammar), 3. Ideas and meanings of mathematics, e.g. applications and metaphors. Non-formal ways of hinting mathematical ideas and meanings, shedding light on both Mathematish and content, are suggested.

  • 284.
    Lennerstad, Håkan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Spectrums of knowledge types: mathematics, mathematics education and praxis knowledge2008In: Proceedings of MADIF6, Swedish Society for Research in Mathematics Education , 2008Conference paper (Refereed)
    Abstract [en]

    Knowledge in different research paradigms is discussed: mathematics, mathematics education and a paradigm of practical knowledge. I argue that the three paradigms as highly distinct, different and important. They try to cope with entirely different types of knowledge, all highly relevant for mathematics teachers.

    While mathematics is deductive and mathematical education is evidence based, practical knowledge is a type of knowledge that professionals in any profession develop by experience and by exchange with other professionals. It is based on experience more than on written text. It is well known that it to a large extent is difficult to articulate. Such knowledge is also essential in important types of mathematical knowledge. We discuss the role played by vagueness in mathematics. We also discuss linguistic mathematics knowledge which typically is present but mostly unformulated, as the mother tongue.

    I argue that mathematics, pedagogy and mathematics education suffers from drawbacks by being strongly rooted in the positivist tradition, in which knowledge can always be expressed in words – otherwise it is not knowledge. Central aspects of teacher’s day-to-day profession are too complicated to be captured in words. However, work has been done to allow such practical knowledge to be formulated among professionals. I would like to sketch a more fluent cooperation between the paradigms, in which the advantages of all the different knowledge types may interact and become increasingly useful to each other.

    For such an idea to reach reality, an efficient meeting form is needed. The Dialogue Seminar is developed precisely to study and communicate difficult-to-articulate practical knowledge among experienced professionals from different areas, using analogue and metaphor as catalysts. This offers mathematicians, mathematics education researchers, mathematics teachers and teacher students, and others, an excellent opportunity to listen in depth to each other, and to have a dialogue. 

  • 285. Lennerstad, Håkan
    The directional display1997Conference paper (Refereed)
    Abstract [en]

    The directional display contains and shows several images-which particular image is visible depends on the viewing direction. This is achieved by packing information at high density on a surface, by a certain back illumination technique, and by explicit mathematical formulas which eliminate projection deformations and make it possible to automate the production of directional displays. The display is illuminated but involves no electronic components. Patent is pending for the directional display. Directional dependency of an image can be used in several ways. One is to achieve three-dimensional effects. In contrast to that of holograms, large size and full color involve no problems. Another application of the technique is to show moving sequences. Yet another is to make a display more directionally independent than conventional displays. It is also possible and useful in several contexts to show different text in different directions with the same display. The features can be combined.

  • 286.
    Lennerstad, Håkan
    Blekinge Institute of Technology, Department of Telecommunications and Mathematics.
    The Geometry of the Directional Display1996Report (Refereed)
    Abstract [en]

    The directional display is a new kind of display which can contain and show several images -which particular image is visible depends on the viewing direction. This is achieved by packing information at high density on a surface, by a certain back illumination technique, and by explicit mathematical formulas which make it possible to automatize the printing of a display to obtain desired effects. The directional dependency of the display can be used in several different ways. One is to achieve three-dimensional effects. In contrast to that of holograms, large size and full color here involve no problems. Another application of the basic technique is to show moving sequences. Yet another is to make a display more directionally independent than today’s displays. Patent is pending for the invention in Sweden.

  • 287.
    Lennerstad, Håkan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    The n -dimensional Stern-Brocot tree2019In: International Journal of Number Theory, ISSN 1793-0421, Vol. 15, no 6, p. 1219-1236Article in journal (Refereed)
    Abstract [en]

    This paper generalizes the Stern-Brocot tree to a tree that consists of all sequences of n coprime positive integers. As for n = 2, each sequence P is the sum of a specific set of other coprime sequences, its Stern-Brocot set B(P), where |B(P)| is the degree of P. With an orthonormal base as the root, the tree defines a fast iterative structure on the set of distinct directions in ℤ+n and a multiresolution partition of S+n-1. Basic proofs rely on a matrix representation of each coprime sequence, where the Stern-Brocot set forms the matrix columns. This induces a finitely generated submonoid SB(n, ℕ) of SL(n, ℕ), and a unimodular multidimensional continued fraction algorithm, also generalizing n = 2. It turns out that the n-dimensional subtree starting with a sequence P is isomorphic to the entire |B(P)|-dimensional tree. This allows basic combinatorial properties to be established. It turns out that also in this multidimensional version, Fibonacci-type sequences have maximal sequence sum in each generation. © 2019 World Scientific Publishing Company.

  • 288.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    The n-dimensional Stern-Brocot tree2012Report (Other academic)
    Abstract [en]

    The n-dimensional Stern-Brocot tree consists of all sequences (p₁, ...,p_{n}) of positive integers with no common multiple. The relatively prime sequences can be generated branchwise from each other by simple vector summation, starting with an ON-base, and controlled by a generalized Euclidean algorithm.The tree induces a multiresolution partition of the first quadrant of the (n-1)-dimensional unit sphere, providing a direction approximation property of a sequence by its ancestors. Two matrix representations are introduced, where in both a matrix contains the parents of a sequence. From one of them the isomorphism of a subtree to the entire tree of dimension equal to the number of parents of the top sequence follows. A form of Fibonacci sequences turn out to be the sequences of fastest growing sums. The construction can be regarded an n-dimensional continued fraction, and it may invite further n-dimesional number theory.

  • 289. Lennerstad, Håkan
    et al.
    Bergsten, Christer
    Matematiska språk2008Collection (editor) (Other academic)
    Abstract [sv]

    Sju författare från olika områden ger sin syn på frågan om matematikens språk. Det är matematikerna Christer Kiselman och Håkan Lennerstad, didaktikerna Christer Bergsten och Madeleine Löwing, lingvisten Östen Dahl, och Bo Göranzon och Lars Mouwitz som är forskare inom forskningsområdet yrkeskunnande och teknologi.

  • 290.
    Lennerstad, Håkan
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Eriksson, Mattias
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    List graphs and distance-consistent node labelings2018In: Electronic Journal of Graph Theory and Applications, ISSN 2338-2287, Vol. 6, no 1, p. 152-165Article in journal (Refereed)
    Abstract [en]

    In this paper we consider node labelings c of an undirected connected graph G = (V,E) with labels (1, 2, ...,|V|), which induce a list distance c(u, v) = |c(v) - c(u)| besides the usual graph distance d(u, v). Our main aim is to find a labeling c so c(u; v) is as close to d(u, v) as possible. For any graph we specify algorithms to find a distance-consistent labeling, which is a labeling c that minimize Σ u,vεV (c(u, v) - d(u, v))2. Such labeliings may provide structure for very large graphs. Furthermore, we define a labeling c fulfilling d(u1, v1) < d(u2, v2) ) c(u1, v1) ⇒ c(u2, v2) for all node pairs u1; v1 and u2; v2 as a list labeling, and a graph that has a list labeling is a list graph. We prove that list graphs exist for all n = |V| and all k = |E|: n - 1 ≤ k ≤ n(n - 1)/2, and establish basic properties. List graphs are Hamiltonian, and show weak versions of properties of path graphs. © 2018 Indonesian Combinatorics Society.

  • 291. Lennerstad, Håkan
    et al.
    Jogréus, Claes
    Serier och transformer2002Book (Other academic)
  • 292.
    Lennerstad, Håkan
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Ljungblad, Ann-Louise
    Matematik och respekt: matematikens mångfald och lyssnandets konst2012Book (Other (popular science, discussion, etc.))
  • 293. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    An Optimal Execution Time Estimate of Static versus Dynamic Allocation in Multiprocessor Systems1992Report (Other academic)
    Abstract [en]

    Consider a multiprocessor with $k$ identical processors, executing parallel programs consisting of $n$ processes. Let $T_s(P)$ and $T_d(P)$ denote the execution times for the program $P$ with optimal static and dynamic allocations respectively, i. e. allocations giving minimal execution time. We derive a general and explicit formula for the maximal execution time ratio $g(n,k)=\max T_s(P)/T_d(P)$, where the maximum is taken over all programs $P$ consisting of $n$ processes. Any interprocess dependency structure for the programs $P$ is allowed, only avoiding deadlock. Overhead for synchronization and reallocation is neglected. Basic properties of the function $g(n,k)$ are established, from which we obtain a global description of the function. Plots of $g(n,k)$ are included. The results are obtained by investigating a mathematical formulation. The mathematical tools involved are essentially tools of elementary combinatorics. The formula is a combinatorial function applied on certain extremal matrices corresponding to extremal programs. It is mathematically complicated but rapidly computed for reasonable $n$ and $k$, in contrast to the np-completeness of the problems of finding optimal allocations.

  • 294. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    Combinatorics for multiprocessor scheduling optimization and other contexts in computer architecture1996Conference paper (Refereed)
    Abstract [en]

    The method described consists of two steps. First, unnecessary programs are eliminated through a sequence of program transformations. Second, within the remaining set of programs, sometimes regarded as matrices, those where all possible combinations of synchronizations occur equally frequently are proven to be extremal. At this stage we obtain a formulation which is simple enough to allow explicit formulas to be derived. It turns out that the same method can be used for obtaining worst-case bounds on other NP-hard problems within computer architecture.

  • 295. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    Decomposing rational numbers2010In: Acta Arithmetica, ISSN 0065-1036, E-ISSN 1730-6264, Vol. 145, no 3, p. 213-220Article in journal (Refereed)
  • 296. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    En annan addition och Stern-Brocots träd2006In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 3, p. 45-48Article in journal (Refereed)
    Abstract [sv]

    När två bråk adderas så adderar man bråkens täljare för sig och nämnare för sig. Så får man väl inte göra? Jodå, det får man, men inte med vanlig addition. Här får vi en glimt av vad följderna blir av denna annorlunda addition.

  • 297.
    Lennerstad, Håkan
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Lundberg, Lars
    Blekinge Institute of Technology, School of Engineering, Department of Systems and Software Engineering.
    Generalizations of the floor and ceiling functions using the Stern-Brocot tree2006Report (Refereed)
    Abstract [en]

    We consider a fundamental number theoretic problem where practial applications abound. We decompose any rational number a/b in c ratios as evenly as possible while maintaining the sum of numerators and the sum of denominators. The minimum and maximum of the ratios give rational estimates of a/b from below and from above. The case c=b gives the usual floor and ceiling functions. We furthermore define the max-min-difference, which is zero iff c≤GCD(a,b), quantifying the distance to relative primality. A main tool for investigating the properties of these quantities is the Stern-Brocot tree, where all positive rational numbers occur in lowest terms and in size order. We prove basic properties such that there is a unique decomposition that gives both the minimum and the maximum. It turns out that this decomposition contains at most three distinct ratios. The problem has arisen in a generalization of the 4/3-conjecture in computer science.

  • 298. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    Guaranteeing Response Times for Aperiodic Tasks in Global Multiprocessor Scheduling2007In: Real-time systems, ISSN 0922-6443, E-ISSN 1573-1383, Vol. 35, no 2, p. 135-151Article in journal (Refereed)
    Abstract [en]

    We provide a constant time schedulability test for an on-line multiprocessor server handling aperiodic tasks. Dhall's effect is avoided by dividing the tasks in two priority classes based on task utilization: heavy and light. We prove that if the load on the multiprocessor server stays below U threshold = 3 - root 7 approximately equals 35.425%, the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. The same number 35.425% is also a threshold for a task to be characterized as heavy. The bound U threshold = 3 - root 7 approximately equals 35.425% is easy-to-use, but not sharp if we know the number of processors in the multiprocessor system. Assuming the server to be equipped with m processors, we calculate a formula for the sharp bound U threshold (m), which converges to U threshold from above as m -> infinity . The results are based on a utilization function u(x) = 2(1 - x)/(2 + root 2+2x). By using this function, the performance of the multiprocessor server can in some cases be improved beyond U threshold(m) by paying the extra overhead of monitoring the individual utilization of the current tasks.

  • 299. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    Optimal combinatorial functions comparing multiprocess allocation performance in multiprocessor systems2000In: SIAM journal on computing (Print), ISSN 0097-5397, E-ISSN 1095-7111, p. 1816-1838Article in journal (Refereed)
    Abstract [en]

    For the execution of an arbitrary parallel program P, consisting of a set of processes with any executable interprocess dependency structure, we consider two alternative multiprocessors. The first multiprocessor has q processors and allocates parallel programs dynamically; i.e., processes may be reallocated from one processor to another. The second employs cluster allocation with k clusters and u processors in each cluster: here processes may be reallocated within a cluster only. Let T-d(P, q) and T-c(P, k, u) be execution times for the parallel program P with optimal allocations. We derive a formula for the program independent performance function [GRAPHICS] Hence, with optimal allocations, the execution of P can never take more than a factor G(k, u, q) longer time with the second multiprocessor than with the first, and there exist programs showing that the bound is sharp. The supremum is taken over all parallel programs consisting of any number of processes. Overhead for synchronization and reallocation is neglected only. We further present a tight bound which exploits a priori knowledge of the class of parallel programs intended for the multiprocessors, thus resulting in a sharper bound. The function g(n, k, u, q) is the above maximum taken over all parallel programs consisting of n processes. The functions G and g can be used in various ways to obtain tight performance bounds, aiding in multiprocessor architecture decisions.

  • 300. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    Optimal Combinatorial Functions Comparing Multiprocess Allocation Performance in Multiprocessor Systems1993Report (Other academic)
    Abstract [en]

    For the execution of an arbitrary parallel program P, consisting of a set of processes, we consider two alternative multiprocessors. The first multiprocessor has q processors and allocates parallel programs dynamically, i.e. processes may be reallocated from one processor to another. The second employs cluster allocation with k clusters and u processors in each cluster - here processes may be reallocated within a cluster only. Let T_d(P,q) and T_c (P,k,u) be execution times for the parallel program P with optimal allocations. We derive a formula for the program independent performance function G(k,u,q)=\sup_ all parallel programs P T_c(P,k,u)}{T_d(P,q)}. Hence, with optimal allocations, the execution of $P$ can never take more than a factor $G(k,u,q)$ longer time with the second multiprocessor than with the first, and there exist programs showing that the bound is sharp. The supremum is taken over all parallel programs consisting of any number of processes. Any interprocess dependency structure is allowed for the parallel programs, except deadlock. Overhead for synchronization and reallocation is neglected only. We further present optimal formulas which exploits a priori knowledge of the class of parallel programs intended for the multiprocessor, thus resulting in sharper optimal bounds. The function g(n,k,u,q) is the above maximum taken over all parallel programs consisting of n processes. The function s(n,v,k,u) is the same maximum, with q=n, taken over all parallel programs of $n$ processes which has a degree of parallelism characterized by a certain parallel profile vector v=(v_1,...,v_n). The functions can be used in various ways to obtain optimal performance bounds, aiding in multiprocessor architecture decisions. An immediate application is the evaluation of heuristic allocation algorithms. It is well known that the problems of finding the corresponding optimal allocations are NP-complete. We thus in effect present a methodology to obtain optimal control of NP-complete scheduling problems.

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