Partition search for non-binary constraint satisfaction

Ullmann, J. R.

doi:10.1016/j.ins.2007.03.030

Cited by 49 publications

(62 citation statements)

References 74 publications

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“…This is because procedure forwardCheck, when called after elective instantiation of an implied-instantiated variable, may remove values from further domains, thus speeding up the search [Ullmann 2007]. Appendix Section A.2 includes this version of procedure choose, and explains how Line 1 in Figure 4 avoids visiting adjacent variables that have not · 9 procedure forwardCheck(in j, v : integer; in out Dsets: array of bit-vectors; out consistent: boolean); input: j identifies the variable that has just been instantiated; v is the value that has been assigned to j by elective instantiation; Bit matrices are accessed via global variables; input and output: Dsets is an array of bit-vectors representing domains; output: consistent = (no domain is empty); begin 1 for each variable Vi adjacent to Vj that has not been electively instantiated do 2…”

Section: A Bit-vector Forward Checking Proceduresmentioning

confidence: 99%

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Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism

Ullmann

2010

ACM J. Exp. Algorithmics

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A solution to a binary constraint satisfaction problem is a set of discrete values, one in each of a given set of domains, subject to constraints that allow only prescribed pairs of values in specified pairs of domains. Solutions are sought by backtrack search interleaved with a process that removes from domains those values that are currently inconsistent with provisional choices already made in the course of search. For each value in a given domain, a bit-vector shows which values in another domain are or are not permitted in a solution. Bit-vector representation of constraints allows bit-parallel, therefore fast, operations for editing domains during search. This article revises and updates bit-vector algorithms published in the 1970's, and introduces focus search, which is a new bit-vector algorithm relying more on search and less on domain-editing than previous algorithms. Focus search is competitive within a limited family of constraint satisfaction problems.Determination of subgraph isomorphism is a specialized binary constraint satisfaction problem for which bit-vector algorithms have been widely used since the 1980's, particularly for matching molecular structures. This article very substantially updates the author's 1976 subgraph isomorphism algorithm, and reports experimental results with random and real-life data.

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Section: A Bit-vector Forward Checking Proceduresmentioning

confidence: 99%

“…Focus search belongs to a family of algorithms that also includes partition search for non-binary constraint satisfaction [Ullmann 2007]. Like focus search, partition search employs a static instantiation sequence 31 and avoids save/restore.…”

Section: Relationship Between Focus Search and Partition Searchmentioning

confidence: 99%

Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism

Ullmann

2010

ACM J. Exp. Algorithmics

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“…We now propose an implementation that only trails one integer, building upon an idea in STR and STR2 [18,11]. The implementation simply keeps invalid elements at the end of the table, with a single variable size representing the boundary between valid (before position size) and invalid elements (after position size).…”

Section: Introductionmentioning

confidence: 99%

An Optimal Filtering Algorithm for Table Constraints

Mairy

Hentenryck

Deville

2012

Lecture Notes in Computer Science

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Abstract. Filtering algorithms for table constraints are constraint-based, which means that the propagation queue only contains information on the constraints that must be reconsidered. This paper proposes four efficient value-based algorithms for table constraints, meaning that the propagation queue also contains information on the removed values. One of these algorithms (AC5TC-Tr) is proved to have an optimal time complexity of O(r.t + r.d) per table constraint. Experimental results show that, on structured instances, all our algorithms are two or three times faster than the state of the art STR2+ and MDD c algorithms.

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“…To enforce the property, known as Generalized Arc Consistency (GAC) on soft table constraints, i.e., soft constraints defined extensionally by listing tuples and their costs, we propose to combine two techniques, namely, Simple Tabular Reduction (STR) [16] and cost transfer. Basically, whenever some domain values are deleted during propagation or search, all tuples that become invalid are removed from constraint tables.…”

Section: Introductionmentioning

confidence: 99%

Propagating Soft Table Constraints

Lecoutre

Paris

Roussel

et al. 2012

Lecture Notes in Computer Science

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Abstract. WCSP is a framework that has attracted a lot of attention during the last decade. In particular, many filtering approaches have been developed on the concept of equivalence-preserving transformations (cost transfer operations), using the definition of soft local consistencies such as, for example, node consistency, arc consistency, full directional arc consistency, and existential directional arc consistency. Almost all algorithms related to these properties have been introduced for binary weighted constraint networks, and most of the conducted experiments typically include networks with binary and ternary constraints only. In this paper, we focus on extensional soft constraints (of large arity), so-called soft table constraints. We propose an algorithm to enforce a soft version of generalized arc consistency (GAC) on such constraints, by combining both the techniques of cost transfer and simple tabular reduction, the latter dynamically maintaining the list of allowed tuples in constraint tables. On various series of problem instances containing soft table constraints of large arity, we show the practical interest of our approach.

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Partition search for non-binary constraint satisfaction

Cited by 49 publications

References 74 publications

Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism

Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism

An Optimal Filtering Algorithm for Table Constraints

Propagating Soft Table Constraints

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