Results 1  10
of
24
Data structures for generalised arc consistency for extensional constraints
 In Proceedings of the Twenty Second Conference on Artificial Intelligence
, 2007
"... Extensional (table) constraints are an important tool for attacking combinatorial problems with constraint programming. Recently there has been renewed interest in fast propagation algorithms for these constraints. We describe the use of two alternative data structures for maintaining generalised ar ..."
Abstract

Cited by 32 (9 self)
 Add to MetaCart
(Show Context)
Extensional (table) constraints are an important tool for attacking combinatorial problems with constraint programming. Recently there has been renewed interest in fast propagation algorithms for these constraints. We describe the use of two alternative data structures for maintaining generalised arc consistency on extensional constraints. The first, the NextDifference list, is novel and has been developed with this application in mind. The second, the trie, is well known but its use in this context is novel. Empirical analyses demonstrate the efficiency of the resulting approaches, both in GACschema, and in the watchedliteral table constraint in Minion.
Tailoring solverindependent constraint models: A case study with essence’ and minion
 In Proceedings of the 7th International Symposium on Abstraction, Reformulation and Approximation
, 2007
"... Abstract. In order to apply constraint programming to a particular domain, the problem must first be modelled as a constraint satisfaction problem. There are typically many alternative models of a given problem, and formulating an effective model requires a great deal of expertise. To reduce this bo ..."
Abstract

Cited by 31 (21 self)
 Add to MetaCart
(Show Context)
Abstract. In order to apply constraint programming to a particular domain, the problem must first be modelled as a constraint satisfaction problem. There are typically many alternative models of a given problem, and formulating an effective model requires a great deal of expertise. To reduce this bottleneck, the Essence language allows the specification of a problem abstractly, i.e. without making modelling decisions. This specification is refined automatically by the Conjure system to a solverindependent constraint modelling language Essence ′. However, there is still significant work involved in translating an Essence ′ model for use with a particular constraint solver. This paper discusses this ‘tailoring’ process with reference to the constraint solver Minion. 1
Breaking Symmetry of Interchangeable Variables and Values
"... A common type of symmetry is when both variables and values partition into interchangeable sets. Polynomial methods have been introduced to eliminate all symmetric solutions introduced by such interchangeability. Unfortunately, whilst eliminating all symmetric solutions is tractable in this case, p ..."
Abstract

Cited by 18 (13 self)
 Add to MetaCart
(Show Context)
A common type of symmetry is when both variables and values partition into interchangeable sets. Polynomial methods have been introduced to eliminate all symmetric solutions introduced by such interchangeability. Unfortunately, whilst eliminating all symmetric solutions is tractable in this case, pruning all symmetric values is NPhard. We introduce a new global constraint called SIGLEX and its GAC propagator for pruning some (but not necessarily all) symmetric values. We also investigate how different postings of the SIGLEX constraints affect the pruning performance during constraint solving. Finally, we test these static symmetry breaking constraints experimentally for the first time.
Symmetries of Symmetry Breaking Constraints
"... Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry class. We use these observations in two methods for eliminating s ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
(Show Context)
Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry class. We use these observations in two methods for eliminating symmetry from a problem. These methods are designed to have many of the advantages of symmetry breaking methods that post static symmetry breaking constraint without some of the disadvantages. In particular, the two methods prune the search space using fast and efficient propagation of posted constraints, whilst reducing the conflict between symmetry breaking and branching heuristics. Experimental results show that the two methods perform well on some standard benchmarks. 1
Breaking Generator Symmetry
, 2009
"... Dealing with large numbers of symmetries is often problematic. One solution is to focus on just symmetries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete, there are also cases where no irredundant generating set eli ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Dealing with large numbers of symmetries is often problematic. One solution is to focus on just symmetries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete, there are also cases where no irredundant generating set eliminates all symmetry. However, focusing on just generators improves tractability. We prove that it is polynomial in the size of the generating set to eliminate all symmetric solutions, but NPhard to prune all symmetric values. Our proof considers row and column symmetry, a common type of symmetry in matrix models where breaking just generator symmetries is very effective. We show that propagating a conjunction of lexicographical ordering constraints on the rows and columns of a matrix of decision variables is NPhard.
Evaluation of LengthLex Set Variables
"... Abstract. This paper presents the first experimental evaluation of the lengthlex domain for set variables. The implementation is based on boundconsistency algorithms proposed in earlier work and two novel technical contributions: a generic filtering algorithm which automatically pushes ordering co ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. This paper presents the first experimental evaluation of the lengthlex domain for set variables. The implementation is based on boundconsistency algorithms proposed in earlier work and two novel technical contributions: a generic filtering algorithm which automatically pushes ordering constraints into symmetric binary constraints with only a logarithmic overhead and an adaptation of symmetrybreaking constraints from 0/1 matrices to the lengthlex ordering. The experimental results indicate that the lengthlex representation for set variables is very effective and robust on traditional setCSPs benchmarks. 1
Parameterized Complexity Results in Symmetry Breaking
, 2010
"... Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into that intractability and help identify special cases in which sy ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into that intractability and help identify special cases in which symmetry can be dealt with more tractably.
Short and Long Supports for Constraint Propagation
"... Specialpurpose constraint propagation algorithms frequently make implicit use of short supports — by examining a subset of the variables, they can infer support (a justification that a variablevalue pair may still form part of an assignment that satisfies the constraint) for all other variables an ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Specialpurpose constraint propagation algorithms frequently make implicit use of short supports — by examining a subset of the variables, they can infer support (a justification that a variablevalue pair may still form part of an assignment that satisfies the constraint) for all other variables and values and save substantial work – but short supports have not been studied in their own right. The two main contributions of this paper are the identification of short supports as important for constraint propagation, and the introduction of HaggisGAC, an efficient and effective general purpose propagation algorithm for exploiting short supports. Given the complexity of HaggisGAC, we present it as an optimised version of a simpler algorithm ShortGAC. Although experiments demonstrate the efficiency of ShortGAC compared with other generalpurpose propagation algorithms where a compact set of short supports is available, we show theoretically and experimentally that HaggisGAC is even better. We also find that HaggisGAC performs better than GACSchema on fulllength supports. We also introduce a variant algorithm HaggisGACStable, which is adapted to avoid work on backtracking and in some cases can be faster and have significant reductions in memory use. All the proposed algorithms are excellent for propagating disjunctions of constraints. In all experiments with disjunctions we found our algorithms to be faster than Constructive Or and GACSchema by at least an order of magnitude, and up to three orders of magnitude. 1.
Symmetry within and between solutions
"... Symmetry can be used to help solve many problems. For instance, Einstein’s famous 1905 paper (”On the Electrodynamics of Moving Bodies”) uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has played an important role in both problem representation and ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Symmetry can be used to help solve many problems. For instance, Einstein’s famous 1905 paper (”On the Electrodynamics of Moving Bodies”) uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has played an important role in both problem representation and reasoning. I describe recent work on using symmetry to help solve constraint satisfaction problems. Symmetries occur within individual solutions of problems as well as between different solutions of the same problem. Symmetry can also be applied to the constraints in a problem to give new symmetric constraints. Reasoning about symmetry can speed up problem solving, and has led to the discovery of new results in both graph and number theory.
Symmetry Breaking by Metaheuristic Search
, 2008
"... Several methods exist for breaking symmetry in constraint problems, but most potentially suffer from high memory requirements, high computational overhead, or both. We describe a new partial symmetry breaking method that can be applied to arbitrary variable/value symmetries. It models dominance dete ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Several methods exist for breaking symmetry in constraint problems, but most potentially suffer from high memory requirements, high computational overhead, or both. We describe a new partial symmetry breaking method that can be applied to arbitrary variable/value symmetries. It models dominance detection as a nonstationary optimisation problem, and solves it by resourcebounded metaheuristic search in the symmetry group. It has low memory requirement and computational overhead, yet in preliminary experiments on BIBD design it breaks most symmetries.