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212
CSPs and Connectedness: P/NPComplete Dichotomy for Idempotent, Right
"... Abstract—In the 1990’s, Jeavons showed that every finite algebra corresponds to a class of constraint satisfaction problems. Vardi later conjectured that idempotent algebras exhibit P/NP dichotomy: Every non NPcomplete algebra in this class must be tractable. Here we discuss how tractability corre ..."
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corresponds to connectivity in Cayley graphs. In particular, we show that dichotomy in finite idempotent, right quasigroups follows from a very strong notion of connectivity. Moreover, P/NP membership is firstorder axiomatizable in involutory quandles. I.
Clustering for Disconnected Solution Sets of Numerical CSPs
 Recent Advances in Constraints: International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2003
"... Abstract. This paper considers the issue of preprocessing the output of intervalbased solvers for further exploitations when solving numerical CSPs with continuum of solutions. Most intervalbased solvers cover the solution sets of such problems with a large collection of boxes. This makes it diffi ..."
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Cited by 1 (1 self)
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Abstract. This paper considers the issue of preprocessing the output of intervalbased solvers for further exploitations when solving numerical CSPs with continuum of solutions. Most intervalbased solvers cover the solution sets of such problems with a large collection of boxes. This makes
Locating the Phase Transition in Binary Constraint Satisfaction Problems
 Artificial Intelligence
, 1994
"... The phase transition in binary constraint satisfaction problems, i.e. the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solutions, as the constraints become tighter, is investigated by examining the behaviour of samples of ..."
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Cited by 134 (4 self)
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The phase transition in binary constraint satisfaction problems, i.e. the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solutions, as the constraints become tighter, is investigated by examining the behaviour of samples of randomlygenerated problems. In contrast to theoretical work, which is concerned with the asymptotic behaviour of problems as the number of variables becomes larger, this paper is concerned with the location of the phase transition in finite problems. The accuracy of a prediction based on the expected number of solutions is discussed; it is shown that the variance of the number of solutions can be used to set bounds on the phase transition and to indicate the accuracy of the prediction. A class of sparse problems, for which the prediction is known to be inaccurate, is considered in detail; it is shown that, for these problems, the phase transition depends on the topology of the constraint gr...
A Practical Guide to the Empirical Evaluation and Comparison of the Performance of Algorithms Operating on CSPs
, 2004
"... This report highlights the important steps in experiment design and setup when conducting experimentations on randomly generated problems. 1 Contents ..."
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This report highlights the important steps in experiment design and setup when conducting experimentations on randomly generated problems. 1 Contents
A NEW COMBINATORIAL APPROACH TO THE CONSTRAINT SATISFACTION PROBLEM DICHOTOMY CLASSIFICATION
"... Abstract. We introduce a new general polynomialtime construction the fibre construction which reduces any constraint satisfaction problem CSP(H) to the constraint satisfaction problem CSP(P), where P is any subprojective relational structure. As a consequence we get a new proof (not using univers ..."
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universal algebra) that CSP(P) is NPcomplete for any subprojective (and so for any projective) relational structure. This provides a starting point for a new combinatorial approach to the NPcompleteness part of the conjectured Dichotomy Classification of CSPs, which was previously obtained by algebraic
A NEW COMBINATORIAL APPROACH TO THE CONSTRAINT SATISFACTION PROBLEM DICHOTOMY CLASSIFICATION
, 2007
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The complexity of acyclic conjunctive queries
 Journal of the ACM
, 1998
"... This paper deals with the evaluation of acyclic Boolean conjunctive queries in relational databases. By wellknown results of Yannakakis [1981], this problem is solvable in polynomial time; its precise complexity, however, has not been pinpointed so far. We show that the problem of evaluating acyc ..."
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Cited by 98 (22 self)
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acyclic Boolean conjunctive queries is complete for LOGCFL, the class of decision problems that are logspacereducible to a contextfree language. Since LOGCFL is contained in AC 1 and NC 2, the evaluation problem of acyclic Boolean conjunctive queries is highly parallelizable. We present a parallel
Logical preference representation and combinatorial vote
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 2002
"... We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of nonindependent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and ..."
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Cited by 90 (16 self)
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We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of nonindependent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and the automated choice of an optimal decision. For each of these issues, we briefly review the state of the art, we try to define the main problems to be solved and identify their computational complexity.
Qualitative Spatial Representation and Reasoning
 An Overview”, Fundamenta Informaticae
, 2001
"... The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related ..."
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Cited by 67 (10 self)
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The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science
Consistency Techniques for Continuous Constraints
 Constraints
, 1996
"... We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constrai ..."
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Cited by 61 (7 self)
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We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.
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