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  • 1.
    Angelsmark, Ola
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Constraints, adjunctions and (Co)algebras2000In: Electronical Notes in Theoretical Computer Science, ISSN 1571-0661, E-ISSN 1571-0661, Vol. 33Conference paper (Other academic)
    Abstract [en]

    The connection between constraints and universal algebra has been looked at in, e.g., Jeavons, Cohen and Pearson, 1998, and has given interesting results. Since the connection between universal algebra and category theory is so obvious, we will in this paper investigate if the usage of category theory has any impact on the results and/or reasoning and if anything can be gained from this approach. We construct categories of problem instances and of solutions to these, and, via an adjunction between these categories, note that the algebras give us a way of describing 'minimality of a problem,' while the coalgebras give a criterion for deciding if a given set of solutions can be expressed by a constraint problem of a given arity. Another pair of categories, of sets of relations and of sets of operations on a fixed set, is defined, and this time the algebras we get give an indication of the 'expressive power' of a set of constraint types, while the coalgebras tell us about the computational complexity of the corresponding constraint problem. © 2000 Published by Elsevier Science B.V.

  • 2.
    Angelsmark, Ola
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Constraints, Adjunctions and (Co)algebras2000In: Coalgebraic Methods in Computer Science CMCS-2000,2000, Science Direct , 2000, p. 3-12Conference paper (Refereed)
    Abstract [en]

    The connection between constraints and universal algebra has been looked at in, e.g Jeavons, Cohen and Pearson, 1998, and has given interesting results. Since the connection between universal algebra and category theory is so obvious, we will in this paper investigate if the usage of category theory has any impact on the results and/or reasoning and if anything can be gained from this approach. We construct categories of problem instances and of solutions to these, and, via an adjunction between these categories, note that the algebras give us a way of describing 'minimality of a problem,' while the coalgebras give a criterion for deciding if a given set of solutions can be expressed by a constraint problem of a given arity. Another pair of categories, of sets of relations and of sets of operations on a fixed set, is defined, and this time the algebras we get give an indication of the 'expressive power' of a set of constraint types, while the coalgebras tell us about the computational complexity of the corresponding constraint problem.

  • 3.
    Angelsmark, Ola
    Linköping University, Department of Computer and Information Science, TCSLAB. Linköping University, The Institute of Technology.
    Constructing Algorithms for Constraint Satisfaction and Related Problems: Methods and Applications2005Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, we will discuss the construction of algorithms for solving Constraint Satisfaction Problems (CSPs), and describe two new ways of approaching them. Both approaches are based on the idea that it is sometimes faster to solve a large number of restricted problems than a single, large, problem. One of the strong points of these methods is that the intuition behind them is fairly simple, which is a definite advantage over many techniques currently in use.

    The first method, the covering method, can be described as follows: We want to solve a CSP with n variables, each having a domain with d elements. We have access to an algorithm which solves problems where the domain has size e < d, and we want to cover the original problem using a number of restricted instances, in such a way that the solution set is preserved. There are two ways of doing this, depending on the amount of work we are willing to invest; either we construct an explicit covering and end up with a deterministic algorithm for the problem, or we use a probabilistic reasoning and end up with a probabilistic algorithm.

    The second method, called the partitioning method, relaxes the demand on the underlying algorithm. Instead of having a single algorithm for solving problems with domain less than d, we allow an arbitrary number of them, each solving the problem for a different domain size. Thus by splitting, or partitioning, the domain of the large problem, we again solve a large number of smaller problems before arriving at a solution.

    Armed with these new techniques, we study a number of different problems; the decision problems (d, l)-CSP and k-Colourability, together with their counting counterparts, as well as the optimisation problems Max Ind CSP, Max Value CSP, Max CSP, and Max Hamming CSP. Among the results, we find a very fast, polynomial space algorithm for determining k-colourability of graphs.

  • 4.
    Angelsmark, Ola
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Partitioning based algorithms for some colouring problems2005In: Proceedings of the Joint Annual Workshop of {ERCIM/CoLogNet} on Constraint Solving and Constraint Logic Programming,2005, ERCIM , 2005, p. 28-42Conference paper (Refereed)
  • 5.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Dahllöf, Vilhelm
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Jonsson, Peter
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Finite Domain Constraint Satisfaction Using Quantum Computation2002In: Mathematical Foundations of Computer Science, 27th International Symposium MFCS-2002,2002, Heidelberg: Springer Verlag , 2002, p. 93-Conference paper (Refereed)
    Abstract [en]

    We present a quantum algorithm for finite domain constraint solving, where the constraints have arity 2. It is complete and runs in time, where d is size of the domain of the variables and n the number of variables. For the case of d=3 we provide a method to obtain an upper time bound of . Also for d=5 the upper bound has been improved. Using this method in a slightly different way we can decide 3-colourability in O(1.2185^n) time.

  • 6.
    Angelsmark, Ola
    et al.
    Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
    Jonsson, Peter
    Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
    Improved algorithms for counting solutions in constraint satisfaction problems2003In: Principles and Practice of Constraint Programming, 9th International Conference CP 2003,2003, Springer, 2003, Vol. 2833, p. 81-95Conference paper (Refereed)
    Abstract [en]

    Counting the number of solutions to CSP instances has vast applications in several areas ranging from statistical physics to artificial intelligence. We provide a new algorithm for counting the number of solutions to binary CSP s which has a time complexity ranging from O ((d/4 . alpha(4))(n)) to O((alpha + alpha(5) + [d/4 - 1] . alpha(4))(n)) (where alpha approximate to 1.2561) depending on the domain size d greater than or equal to 3. This is substantially faster than previous algorithms, especially for small d. We also provide an algorithm for counting k-colourings in graphs and its running time ranges from O ([log(2) k](n)) to O ([log(2) k + 1](n)) depending on k greater than or equal to 4. Previously, only an O(1.8171(n)) time algorithm for counting 3-colourings were known, and we improve this upper bound to O(1.7879(n)).

  • 7.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Jonsson, Peter
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Linusson, Svante
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Determining the Number of Solutions to Binary CSP Instances2002In: Principles and Practice of Constraint Programming, 8th International Conference CP-2002,2002, Heidelberg: Springer Verlag , 2002, p. 327-Conference paper (Refereed)
    Abstract [en]

    Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2-SAT instances, where the total number of solutions to these instances is the same as those of the original problem. The algorithm consists of two main cases, depending on whether the domain size d is even, in which case the algorithm runs in O(1.3247^n*(d/2)^n) time, or odd, in which case it runs in O(1.3247^n*((d^2+d+2)/4)^(n/2)) if d=4*k+1, and O(1.3247^n*((d^2+d)/4)^(n/2)) if d=4*k+3. We also give an algorithm for counting the number of possible 3-colourings of a given graph, which runs in O(1.8171^n), an improvement over our general algorithm gained by using problem specific knowledge. 

  • 8.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    A Microstructure Based Approach to Constraint Satisfaction Optimisation Problems2005In: The 18th International FLAIRS Conference,2005, Menlo Park, CA, USA: AAAI Press , 2005, p. 155-Conference paper (Refereed)
    Abstract [en]

    We study two constraint satisfaction optimisation problems: The Max Value problem for CSPs, which, somewhat simplified, aims at maximising the sum of the (weighted) variable values in the solution, and the Max Ind problem, where the goal is to find a satisfiable subinstance of the original instance containing as many variables as possible. Both problems are NP-hard to approximate within n^(1-e), e>0, where n is the number of variables in the problems, which implies that it is of interest to find exact algorithms. By exploiting properties of the microstructure, we construct algorithms for solving instances of these problems with small domain sizes, and then, using a probabilistic reasoning, we show how to get algorithms for more general versions of the problems. The resulting algorithms have running times of O((0.585d)^n) for Max Value (d,2)-CSP, and O((0.503d)^n) for MaxInd (d,2)-CSP. Both algorithms represent the best known theoretical bounds for their respective problem, and, more importantly, the methods used are applicable to a wide range of optimisation problems. 

  • 9.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Algorithms for the maximum hamming distance problem2006In: Recent Advances in Constraints: Joint ERCIM/CoLogNET International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2005, Uppsala, Sweden, June 20-22, 2005, Revised Selected and Invited Papers / [ed] Boi V. Faltings, Adrian Petcu, François Fages and Francesca Rossi, Springer Berlin/Heidelberg, 2006, Vol. 3419, p. 128-141Chapter in book (Refereed)
    Abstract [en]

    This book constitutes the thoroughly refereed and extended post-proceedings of the Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2005, held in Uppsala, Sweden in June 2005.

    Besides papers taken from the workshop, others are submitted in response to an open call for papers after the workshop.

    The 12 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on global constraints, search and heuristics, language and implementation issues, and modeling

  • 10.
    Angelsmark, Ola
    et al.
    Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
    Thapper, Johan
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Algorithms for the Maximum Hamming Distance Problem2006In: Recent Advances in Constraints: Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2004, Lausanne, Switzerland, June 23-25, 2004, Revised Selected and Invited Papers / [ed] Boi V. Faltings, Adrian Petcu, François Fages and Francesca Rossi, Springer Berlin/Heidelberg, 2006, p. 128-141Chapter in book (Refereed)
    Abstract [en]

    This book constitutes the thoroughly refereed and extended post-proceedings of the Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2005, held in Uppsala, Sweden in June 2005.

    Besides papers taken from the workshop, others are submitted in response to an open call for papers after the workshop.

    The 12 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on global constraints, search and heuristics, language and implementation issues, and modeling.

  • 11.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    New Algorithms for the Maximum Hamming Distance Problem2004In: Joint Annual Workshop of ERCIMCoLogNet on Constraint Solving and Constraint Logic Programming,2004, 2004, p. 271-285Conference paper (Refereed)
  • 12.
    Angelsmark, Ola
    et al.
    Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
    Thapper, Johan
    Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
    Partitioning based algorithms for some colouring problems2006In: Recent Advances in Constraints / [ed] Brahim Hnich, Mats Carlsson, François Fages and Francesca Rossi, Springer Berlin/Heidelberg, 2006, Vol. 3978, p. 44-58Chapter in book (Refereed)
    Abstract [en]

    This book constitutes the thoroughly refereed and extended post-proceedings of the Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2005, held in Uppsala, Sweden in June 2005.

    Besides papers taken from the workshop, others are submitted in response to an open call for papers after the workshop.

    The 12 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on global constraints, search and heuristics, language and implementation issues, and modeling.

1 - 12 of 12
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