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Improved algorithms for the global cardinality constraint

引用

10th international conference on principles and practice of constraint programming, cp 2004

作者： Quimper, Claude-Guy López-Ortiz, Alejandro Van Beek, Peter Golynski, Alexander University of Waterloo Waterloo Canada

ISBN: (纸本)3540232419

We study the global cardinality constraint (gcc) and propose an O(n1.5d) algorithm for domain consistency and an O(cn + dn) algorithm for range consistency where n is the number of variables, d the number of values in the domain, and c an output dependent variable smaller than or equal to n. We show how to prune the cardinality variables in O(n2d + n2.66) steps, detect if gcc is universal in constant time and prove that it is NP-Hard to maintain domain consistency on extended-GCC. © Springer-Verlag Berlin Heidelberg 2004.

关键词： Computer programming

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constraint propagation for soft constraints: Generalization and termination conditions 6th

引用

6th international conference on principles and practice of constraint programming, cp2000

作者： Bistarelli, S. Gennari, R. Rossi, F. Università di Pisa Dipartimento di Informatica Corso Italia 40 Pisa56125 Italy ILLC Institute of Logic Language and Computation University of Amsterdam N. Doelenstraat 15 Amsterdam1012 CP Netherlands Università di Padova Dipartimento di Matematica Pura ed Applicata Via Belzoni 7 Padova35131 Italy

ISBN: (纸本)3540410538

Soft constraints based on semirings are a generalization of classical constraints, where tuples of variables’ values in each soft constraint are uniquely associated to elements from an algebraic structure called semiring. this framework is able to express, for example, fuzzy, classical, weighted, valued and over-constrained constraint problems. Classical constraint propagation has been extended and adapted to soft constraints by defining a schema for soft local consistency [BMR97]. On the other hand, in [Apt99a,Apt99b] it has been proved that most of the well known constraint propagation algorithms for classical constraints can be cast within a single schema. In this paper we combine these two schema and we show how the framework of [Apt99a,Apt99b] can be used for soft constraints. In doing so, we generalize the concept of soft local consistency, and we prove some convenient properties about its termination. © Springer-Verlag Berlin Heidelberg 2000.

关键词： constraint theory

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Improved bound computation in presence of several clique constraints

引用

10th international conference on principles and practice of constraint programming, cp 2004

作者： Puget, Jean-Francois ILOG 9 avenue de Verdun Gentilly94253 France

ISBN: (纸本)3540232419

Bound consistency can easily and efficiently be enforced on linear constraint. However, bound consistency techniques deal with every constraint separately. We show that in some cases much stronger bounds can be computed by looking globally at the set of linear constraints. A simple algorithm for computing such bounds is derived from a new decomposition scheme. We prove that these bounds can be as tight as possible. In some cases this can be better than the standard reduced cost fixings. this algorithm has been implemented within a global constraint. Experimental results on balanced incomplete block design (BIBD) show its effectiveness: we were able to significantly improve over the best published results for this class of problems. © Springer-Verlag Berlin Heidelberg 2004.

关键词： constraint theory

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Symmetry breaking constraints for value symmetries in constraint satisfaction

Symmetry breaking constraints for value symmetries in constr...

引用

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

作者： Law, Y. C. Lee, J. H. M. Chinese Univ Hong Kong Dept Comp Sci & Engn Shatin Hong Kong Peoples R China

constraint satisfaction problems (CSPs) sometimes contain both variable symmetries and value symmetries, causing adverse effects on CSP solvers based on tree search. As a remedy, symmetry breaking constraints are commonly used. While variable symmetry breaking constraints can be expressed easily and propagated efficiently using lexicographic ordering, value symmetry breaking constraints are often difficult to formulate. In this paper, we propose two methods of using symmetry breaking constraints to tackle value symmetries. First, we show theoretically when value symmetries in one CSP correspond to variable symmetries in another CSP of the same problem. We also show when variable symmetry breaking constraints in the two CSPs, combined using channeling constraints, are consistent. Such results allow us to tackle value symmetries efficiently using additional CSP variables and channeling constraints. Second, we introduce value precedence, a notion which can be used to break a common class of value symmetries, namely symmetries of indistinguishable values. While value precedence can be expressed using inefficient if-then constraints in existing CSP solvers, we propose efficient propagation algorithms for implementing global value precedence constraints. We also characterize several theoretical properties of the value precedence constraints. Extensive experiments are conducted to verify the feasibility and efficiency of the two proposals.

关键词： symmetry breaking value symmetries constraint satisfaction

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A constraint-based graphics library for B-Prolog

引用

10th international conference on principles and practice of constraint programming, cp 2004

作者： Zhou, Neng-Fa The City University of New York Afany Software United States

ISBN: (纸本)3540232419

CGLIB is a high-level graphics library for B-Prolog, a constraint logic programming system. the library provides primitives for creating and manipulating graphical objects and a set of constraints including non-overlap, grid, table, and tree constraints that facilitates the specification of the layouts of objects. the library adopts a construct called action rules available in B-Prolog for creating agents and programming interactions among agents or between agents and the user. the library is a fully working system implemented in B-Prolog, Java and C. It can be used in many areas such as drawing editors, interactive user interfaces, document authoring, animation, information visualization, intelligent agents, and games. the high-level abstraction of the library and the use of constraints and action rules in the specification of layouts and behaviors can significantly enhance the productivity of the development of graphics. We demonstrate through several examples the effectiveness of the library as a tool for developing graphics-rich and interactive user interfaces. the system is available from *** and the details of the library can be found in [1].

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Solving finite domain constraint hierarchies by local consistency and tree search

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9th international conference on principles and practice of constraint programming, cp 2003

作者： Bistarelli, Stefano Codognet, Philippe Hui, Kin-Chuen Lee, Jimmy Ho Man Istituto di Informatica e Telematica CNR Pisa Italy Dipartimento di Scienze Universitá degli Studi ‘G. D’annunzio’ di Chieti-Pescara Italy Department of Computer Science University of Paris 6 France Department of Computer Science and Engineering The Chinese University of Hong Kong Hong Kong

ISBN: (纸本)3540202021

We provide a reformulation of the constraint hierarchies (CHs) framework based on the notion of error indicators. Adapting the generalized view of local consistency in semiring-based constraint satisfaction problems (SCSPs), we define constraint hierarchy k-consistency (CH-k-C) and give a CH-2-C enforcement algorithm. We demonstrate how the CH-2-C algorithm can be seamlessly integrated into the ordinary branch-and-bound algorithm to make it a finite domain CH solver. Experimentation confirms the efficiency and robustness of our proposed solver prototype. Unlike other finite domain CH solvers, our proposed method works for both local and global comparators. In addition, our solver can support arbitrary error functions. © Springer-Verlag Berlin Heidelberg 2003.

关键词： constraint satisfaction problems

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Unary resource constraint with optional activities

引用

10th international conference on principles and practice of constraint programming, cp 2004

作者： Vilím, Petr Barták, Roman Čepek, Ondřej Charles University Malostranské náměstí 2/25 Praha 1 Czech Republic Institute of Finance and Administration VŠFS Czech Republic

ISBN: (纸本)3540232419

Scheduling is one of the most successful application areas of constraint programming mainly thanks to special global constraints designed to model resource restrictions. Among these global constraints, edge-finding filtering algorithm for unary resources is one of the most popular techniques. In this paper we propose a new O(n log n) version of the edge-finding algorithm that uses a special data structure called Θ- Λ-tree. this data structure is especially designed for "what-if" reasoning about a set of activities so we also propose to use it for handling so called optional activities, i.e. activities which may or may not appear on the resource. In particular, we propose new O(n log n) variants of filtering algorithms which are able to handle optional activities: overload checking, detectable precedences and not-first/not-last. © Springer-Verlag Berlin Heidelberg 2004.

关键词： Data structures

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Speeding up constraint propagation

引用

10th international conference on principles and practice of constraint programming, cp 2004

作者： Schulte, Christian Stuckey, Peter J. IMIT KTH – Royal Institute of Technology Sweden Dept. of Comp. Sci. and Soft. Eng Univ. of Melbourne Australia

ISBN: (纸本)3540232419

this paper presents a model and implementation techniques for speeding up constraint propagation. Two fundamental approaches to improving constraint propagation are explored: keeping track of which propagators are at fix-point, and choosing which propagator to apply next. We show how idempotence reasoning and events help track fix-points more accurately. We improve these methods by using them dynamically (taking into account current domains to improve accuracy). We define priority-based approaches to choosing a next propagator and show that dynamic priorities can improve propagation. We illustrate that the use of multiple propagators for the same constraint can be advantageous with priorities, and introduce staged propagators which combine the effects of multiple propagators with priorities for greater efficiency. © Springer-Verlag Berlin Heidelberg 2004.

关键词： constraint theory

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constraints for breaking more row and column symmetries

引用

9th international conference on principles and practice of constraint programming, cp 2003

作者： Frisch, Alan M. Jefferson, Chris Miguel, Ian Artificial Intelligence Group Department of Computer Science University of York York United Kingdom

ISBN: (纸本)3540202021

constraint programs containing a matrix of two (or more) dimensions of decision variables often have row and column symmetries: in any assignment to the variables the rows can be swapped and the columns can be swapped without affecting whether or not the assignment is a solution. this introduces an enormous amount of redundancy when searching a space of partial assignments. It has been shown previously that one can remove consistently some of these symmetries by extending such a program with constraints that require the rows and columns to be lexicographically ordered. this paper identifies and studies the properties of a new additional constraint—the first row is less than or equal to all permutations of all other rows—that can be added consistently to break even more symmetries. Two alternative implementations of this stronger symmetry-breaking method are investigated, one of which employs a new algorithm that in time linear in the size of the matrix enforces the constraint that the first row is less than or equal to all permutations of all other rows. It is demonstrated experimentally that our method for breaking more symmetries substantially reduces search effort. © Springer-Verlag Berlin Heidelberg 2003.

关键词： constraint theory

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Improving backtrack search for solving the TCSP

引用

9th international conference on principles and practice of constraint programming, cp 2003

作者： Xu, Lin Choueiry, Berthe Y. Constraint Systems Laboratory Department of Computer Science and Engineering University of Nebraska-Lincoln LincolnNE United States

ISBN: (纸本)3540202021

In this paper, we address the task of finding the minimal network of a Temporal constraint Satisfaction Problem (TCSP).We report the integration of three approaches to improve the performance of the exponential-time backtrack search (BT-TCSP) proposed by Dechter et al. [6] for this purpose. the first approach consists of using a new efficient algorithm (∆STP) [21] for solving the Simple Temporal Problem (STP), an operation that must be executed at each node expansion during BT-TCSP. the second approach improves BT-TCSP itself by exploiting the topology of the temporal network. this is accomplished in three ways: finding and exploiting articulation points (AP), checking the graph for new cycles (NewCyc), and using a newheuristic for edge ordering (EdgeOrd). the third approach is a filtering algorithm, ∆AC, which is used as a preprocessing step to BT-TCSP, and which significantly reduces the size of the TCSP [22]. In addition to introducing two new techniques, NewCyc and EdgeOrd, this paper discusses an extensive evaluation of the merits of the above three approaches. Our experiments on randomly generated problems demonstrate significant improvements in the number of nodes visited, constraint checks, and cpU time. © Springer-Verlag Berlin Heidelberg 2003.

关键词： constraint satisfaction problems

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