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Symmetry and consistency

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Gent, Ian P. Kelsey, Tom Linton, Steve Roney-Dougal, Colva School of Computer Science University of St Andrews St Andrews Fife KY16 9SX United Kingdom

ISBN: (纸本)3540292381

We introduce a novel and exciting research area: symmetrising levels of consistency to produce stronger forms of consistency and more efficient mechanisms for establishing them. We propose new levels of consistency for constraint Satisfaction Problems (CSPs) incorporating the symmetry group of a CSP. We first define Sym(i, j)-consistency, show that even Sym(1,0)-consistency can prune usefully, and study some consequences of maintaining Sym(i, 0)-consistency. Weconsistency then present pseudocode for SymPath consistency, and a symmetrised version of singleton consistency, before presenting experimental evidence of these algorithms' practical effectiveness. With this contribution we establish the study of symmetry-based levels of consistency of CSPs. © Springer-Verlag Berlin Heidelberg 2005.

关键词： Computer science

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Automatic detection of variable and value symmetries

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Puget, Jean-François ILOG 9 avenue de Verdun 94253 Gentilly France

ISBN: (纸本)3540292381

Many symmetry breaking techniques assume thai;the symmetries of a CSP are given as input in addition to the CSP itself. We present a method that can be used to detect all the symmetries of a CSP. this method constructs a graph that has the same symmetries as the CSP. then, generators for the symmetry group are computed using a graph automorphism algorithm. this method improves and extends previous work in order to cover global constraints, arithmetic expressions and value symmetries. We show that this method is able to find symmetries for examples that were thought to be too convoluted for automated detection. We also show that the overhead of symmetry detection is quite negligible, even on very large instances. We present a. comprehensive set of examples where automated symmetry detection is coupled with symmetry breaking techniques. © Springer-Verlag Berlin Heidelberg 2005.

关键词： constraint theory

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Caching search states in permutation problems

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11th international conference on principles and practice of constraint programming - CP 2005

作者： Smith, Barbara M. Cork Constraint Computation Centre University College Cork Ireland

ISBN: (纸本)3540292381

When the search for a solution to a constraint satisfaction problem backtracks, it is not usually worthwhile to remember the assignment that failed, because the same assignment will not occur again. However, we show that for some problems recording assignments is useful, because other assignments can lead to the same state of the search. We demonstrate this in two classes of permutation problem, a satisfaction problem arid an optimization problem. Caching states visited has proved effective in reducing both search effort and run-time for difficult instances of each class, and the space requirements are manageable. © Springer-Verlag Berlin Heldelberg 2005.

关键词： constraint theory

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Preference reasoning

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Rossi, Francesca Domshlak, C. Pini, M.S. Prestwich, S. Sperduti, A. Venable, K.B. Walsh, T. Yorke-Smith, N. Department of Pure and Applied Mathematics University of Padova Italy

ISBN: (纸本)3540292381

constraints and preferences are ubiquitous in real-life. Moreover, preferences can be of many kinds: qualitative, quantitative, conditional, positive or negative, to name a few. Our ultimate goal is to define and study formalisms that can model problems with both constraints and many kind of preferences, possibly defined by several agents, and to develop tools to solve such problems efficiently. © Springer-Verlag Berlin Heidelberg 2005.

关键词： constraint theory

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AND/OR branch-and-bound for solving mixed integer linear programming problems

引用

11th international conference on principles and practice of constraint programming (CP 2005)

作者： Marinescu, R Dechter, R Univ Calif Irvine Irvine CA 92697 USA

ISBN: (纸本)3540292381

Graphical models are a powerful representation framework for automated reasoning tasks. these models use graphs to capture conditional independencies between variables, allowing for a concise representation of the knowledge. Optimization tasks defined within this framework are typically tackled with either search or inference. Search methods are time exponential in the number of variables and can operate in linear space. Inference algorithms are time and space exponential in the tree width of the problem. this potentially higher space complexity makes these methods impractical. the AND/OR search space for graphical models is a newly introduced framework for search that is sensitive to the independencies in the model, often resulting in exponentially reduced complexities. the AND/OR search is based on a pseudo-tree which expresses independencies between variables, resulting in a search tree exponential in the depth of the pseudo-tree, rather than the number of variables. the AND/OR Branch-and-Bound algorithm (AOBB) is a new search method that explores the AND/OR search tree for solving optimization tasks in graphical models. In this paper we extend the algorithm for solving combinatorial optimization problems from the class of Mixed Integer Linear Programs (MILP). A MILP instance is a linear program where some of the decision variables are constrained to have only integer values at the optimal solution (we consider only binary integer variables). AOBB can be readily adapted for solving this class of optimization problems by arranging the integer variables into a start pseudo-tree and, then, traversing the corresponding AND/OR search tree. this rather straightforward extension can be further improved. We introduce a dynamic version of AOBB which uses a recursive decomposition of the problem, based on hypergraph separators. the hypergraph of a MILP instance has a vertex for each constraint and a hyperedge, which corresponds to a variable, connects all the constraints t

关键词： Integer programming

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Search heuristics and heavy-tailed behaviour

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11th international conference on principles and practice of constraint programming (CP 2005)

作者： Hulubei, T O'Sullivan, B Natl Univ Ireland Univ Coll Cork Cork Constraint Computat Ctr Dept Comp Sci Cork Ireland

ISBN: (纸本)3540292381

the heavy-tailed phenomenon that characterises the runtime distributions of backtrack search procedures has received considerable attention over the past few years. Some have conjectured that heavy-tailed behaviour is largely due to the characteristics of the algorithm used. Others have conjectured that problem structure is a significant contributor. In this paper we attempt to explore the former hypothesis, namely we study how variable and value ordering heuristics impact the heavy-tailedness of runtime distributions of backtrack search procedures. We demonstrate that heavy-tailed behaviour can be eliminated from particular classes of random problems by carefully selecting the search heuristics, even when using chronological backtrack search. We also show that combinations of good search heuristics can eliminate heavy tails from Quasigroups with Holes of order 10, and give some insights into why this is the case. these results motivate a more detailed analysis of the effects that variable and value ordering can have on heavy-tailedness. We show how combinations of variable and value ordering heuristics can result in a runtime distribution being inherently heavytailed. Specifically, we show that even if we were to use an Oracle to refute insoluble subtrees optimally, for some combinations of heuristics we would still observe heavy-tailed behaviour. Finally, we study the distributions of refutation sizes found using different combinations of heuristics and gain some further insights into what characteristics tend to give rise to heavy-tailed behaviour.

关键词： Heuristic methods

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Parallel local search in cornet

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Michel, Laurent Van Hentenryck, Pascal University of Connecticut Storrs CT 06269-2155 Brown University Box 1910 Providence RI 02912

ISBN: (纸本)3540292381

the availability of commodity multiprocessors offers significant opportunities for addressing the increasing computational requirements of optimization applications. To leverage these potential benefits, it is important however to make parallel processing easily accessible to a wide audience of optimization programmers. this paper addresses this challenge by proposing parallel programming abstractions that keep the distance between sequential and parallel local search algorithms as small as possible. the abstractions, that include parallel loops, interruptions, and thread pools, are compositional and cleanly separate the optimization program and the parallel instructions. they have been evaluated experimentally on a variety of applications, including facility location and coloring, for which they provide significant speedups. © Springer-Verlag Berlin Heidelberg 2005.

关键词： Computer systems programming

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Asymmetric distributed constraints satisfaction problems

引用

11th international conference on principles and practice of constraint programming (CP 2005)

作者： Zivan, R Meisels, A Ben Gurion Univ Negev Dept Comp Sci IL-84105 Beer Sheva Israel

ISBN: (纸本)3540292381

Distributed constraint satisfaction problems (DisCSPs) with asymmetric constraints reflect the fact that agents may wish to retain their constraints private. Brito and Meseguer proposed a model for asymmetric constraints which they term Partially Known constraints (PKC). In the PKC model each binary constraint is divided between the two constraining agents. In order to solve the resulting DisCSP with asymmetric constraints, a two phase asynchronous backtracking algorithm was proposed [?]. In the first phase an asynchronous backtracking algorithm is performed, in which only the constraints held by the lower priority agents are examined. When a solution is reached, a second phase is performed in which the consistency of the solution is checked again, according to the constraints held by the higher priority agents in each binary constraint. the present paper proposes a one phase asynchronous backtracking algorithm which solves DisCSPs with asymmetric constraints. In the proposed asynchronous backtracking for asymmetric constraints algorithm (ABT_ASC) agents send their proposed assignments to all their neighbors in the constraints graph. Agents assign their local variables according to the priority order as in ABT but check the constraints also against the assignment of lower priority agents. When an agent detects a conflict between its own assignment and the assignment of an agent with a lower priority than itself, it sends a Nogood to the lower priority agent but keeps its assignment. Agents which receive a Nogood from higher priority agents, perform the same operations as if they have produced this Nogood themselves. As in ABT [?], they remove their current assignment from their current-domain, store the eliminating N ogood and reassign their variable. the ABT_ASC algorithm is evaluated experimentaly on randomly generated DisCSPs and is shown to outperform the 2-phase ABT with respect to two different distributed performance measures. ABT_ASC performs fewer non-concu

关键词： constraint theory

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Interactive reconfiguration in power supply restoration

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Hadzic, Tarik Andersen, Henrik Reif Department of Innovation IT University of Copenhagen

ISBN: (纸本)3540292381

Given a configuration of parameters that satisfies a set of constraints, and given external changes that change and fix the value of some parameters making the configuration invalid, the problem of interactive reconfiguration is to assist a user to interactively reassign a subset of the parameters to reach a consistent configuration again. In this paper, we present two BDD-based algorithms for solving the problem, one based on a monolithic BDD-representation of the solution space and another using a set of BDDs. We carry out experiments on a set of power supply restoration benchmarks and show that the set-of-BDDs algorithm scales much better. © Springer-Verlag Berlin Heidelberg 2005.

关键词： constraint theory

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Towards the systematic generation of channelling constraints

引用

11th international conference on principles and practice of constraint programming (CP 2005)

作者： Martínez-Hernández, B Frisch, AM Univ York Dept Comp Sci Artificial Intelligence Grp York YO10 5DD N Yorkshire England

the automatic modelling tool CONJURE [1] generates CSP models from a problem specified in the specification language ESSENCE1. Variables in ESSENCE may have domains currently unsupported by solvers. Also, the elements... 详细信息

ISBN: (纸本)3540292381

the automatic modelling tool CONJURE [1] generates CSP models from a problem specified in the specification language ESSENCE¹. Variables in ESSENCE may have domains currently unsupported by solvers. Also, the elements of the domains may be arbitrarily compound, for example, sets of sets, sets of sets of sets. CONJURE uses a set of refinement rules to compositionally transform the variables (and constraints) into representations that can be implemented in current solvers. CONJURE can produce multiple alternative (redundant) representations of the same variable that may appear simultaneously in the same model. Currently, CONJURE does not generate the channelling constraints [2] that are needed to maintain the consistency between these simultaneous alternatives. there are several unsolved issues related to channeling constraints and automatic modelling, such as, how to identify the cases where a channelled model performs better than a non-channelled one, and how to implement the channelling constraints efficiently. In this paper however, we focus the automated generation of channelling constraints under the CONJURE framework. Our work has identified and proved correct, an algorithm to systematically generate the channelling constraints needed in a CONJURE-generated model. We briefly describe this algorithm as follows. Let P be a specification refined by CONJURE into the CSP model P′. Let X be a variable in P that has two representations X₁ and X₂ in P′. Let Y be a new variable with exactly the same domain of X. We can then re-refine X = Y (channelling constraint between X arid Y) forcing the X to refine into X₁ and the Y into X₂. Hence, we produce a correct channelling constraint between X₁ and X₂ providing CONJURE generates correct refinements. © Springer-Vorlag Berlin Heidelberg 2005.

关键词： constraint theory

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