STR3: A path-optimal filtering algorithm for table constraints

Abstract. We introduce GAC-4R, MDD-4, and MDD-4R three new algorithms for maintaining arc consistency for table and MDD constraints. GAC-4R improves the well-known GAC-4 algorithm by managing the internal data structures in a different way. Instead of maintaining the internal data structures only by studying the consequences of deletions, we propose to reset the data structures by recomputing them from scratch whenever it saves time. This idea avoids the major drawback of the GAC-4 algorithm, i.e., its cost at a shallow searchtree depth. We also show that this idea can be exploited in MDD constraints. Experiments show that GAC-4R is competitive with the best arc-consistency algorithms for table constraints, and that MDD-4R clearly outperforms all classical algorithms for table or MDD constraints.

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“…It has been successfully used in CP for representing sets or lists [8,7,14,15]. We will use it in GAC-4R and MDD-4R, so we give details of it.…”

Section: Sparse Setmentioning

confidence: 99%

“…Some algorithms are lazy (e.g., GAC-Schema [3], STR-2 [14], or STR-3 [15]). They try to reduce the operations executed at each modification (i.e., deletion of value of a domain) at the cost of increasing the complexity of the implementation.…”

Section: Introductionmentioning

confidence: 99%

Improving GAC-4 for Table and MDD Constraints

Perez

Régin

2014

Lecture Notes in Computer Science

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“…Living-STR is similar to STR3 in that it iterates over variable-value pairs rather than over tuples. However, it does not use as much book-keeping for optimizing the number of STR checks as STR3 [14]. Instead, Living-STR uses the same data structures as STR and STR2(+) to manage tuple deletions in a relation [13,21].…”

Section: Algorithm For Enforcing Apc-lcmentioning

confidence: 99%

“…GAC can be enforced by removing domain values that have no GAC-support, leaving the relations unchanged. Simple Tabular Reduction (STR) algorithms not only enforce GAC on the domains, but also remove all tuples τ ∈ R j where ∃x i ∈ scope(R j ) such that τ [x i ] / ∈ dom(x i ) [21,13,14].…”

Section: Local Consistency Propertiesmentioning

confidence: 99%

Adaptive Parameterized Consistency for Non-binary CSPs by Counting Supports

Woodward

Schneider

Choueiry

et al. 2014

Lecture Notes in Computer Science

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Abstract.Determining the appropriate level of local consistency to enforce on a given instance of a Constraint Satisfaction Problem (CSP) is not an easy task. However, selecting the right level may determine our ability to solve the problem. Adaptive parameterized consistency was recently proposed for binary CSPs as a strategy to dynamically select one of two local consistencies (i.e., AC and maxRPC). In this paper, we propose a similar strategy for non-binary table constraints to select between enforcing GAC and pairwise consistency. While the former strategy approximates the supports by their rank and requires that the variables domains be ordered, our technique removes those limitations. We empirically evaluate our approach on benchmark problems to establish its advantages.

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“…Algorithm 6 initializes STR2w's data structures and is executed only once, right after GAC preprocessing. Because STR2w requires tables to be free of invalid tuples before the search starts, it cannot be used as a standalone GAC algorithm and must be used exclusively during search [6,8]. During the initialization, unsupported[x] is set to be the whole domain of x (line 2), while watch is set to empty (line 3).…”

mentioning

confidence: 99%

Improving the lower bound of simple tabular reduction

2014

Self Cite

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Simple Tabular Reduction (STR) is a state-of-the-art filtering technique for enforcing Generalized Arc Consistency (GAC) on positive table constraints. Despite its good performance in practice, the STR2 algorithm suffers from a mandatory lower bound equal to the number of domain values in the current state of the problem, because the presence of each value must be justified every time STR2 is called. We overcome this fixed cost by redesigning STR2 and incorporating watched tuples. Experiments show that the revised algorithm is better at coping with problems that involve a large number of small changes during search and it can be more than twice as fast on certain structured problems.

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STR3: A path-optimal filtering algorithm for table constraints

Cited by 30 publications

References 19 publications

Improving GAC-4 for Table and MDD Constraints

Improving GAC-4 for Table and MDD Constraints

Adaptive Parameterized Consistency for Non-binary CSPs by Counting Supports

Improving the lower bound of simple tabular reduction

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