Revisiting Neighborhood Inverse Consistency on Binary CSPs

Woodward, Robert J.; Karakashian, Shant; Choueiry, Berthe Y.; Bessière, Christian

doi:10.1007/978-3-642-33558-7_50

Cited by 7 publications

(4 citation statements)

References 14 publications

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“…5, refutes our two-cliques hypothesis but reveals the existence of a few large cycles as well as many cycles of size three or more. Previous work argued that the presence of cycles can be detrimental to the effectiveness of constraint propagation and showed how triangulation of the constraint network allows us to remedy the situation [43,44,47]. With this insight, we consider enforcing, during search, Partial Path Consistency (PPC) instead of GAC because the algorithm for PPC operates on existing triangles and on triangulated cycles of the constraint network [8].…”

Section: Illustrative Example: Analyzing Structurementioning

confidence: 99%

Visualizations to Summarize Search Behavior

Howell

Choueiry

2020

Lecture Notes in Computer Science

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In this paper, we argue that metrics that assess the performance of backtrack search for solving a Constraint Satisfaction Problem should not be visualized and examined only at the end of search, but their evolution should be tracked throughout the search process in order to provide a more complete picture of the behavior of search. We describe a process that organizes search history by automatically recognizing qualitatively significant changes in the metrics that assess search performance. To this end, we introduce a criterion for quantifying change between two time instants and a summarization technique for organizing the history of search at controllable levels of abstraction. We validate our approach in the context of two algorithms for enforcing consistency: one that is activated by a surge of backtracking and the second that modifies the structure of the constraint graph. We also introduce a new visualization for exposing the behavior of variable ordering heuristics and validate its usefulness both as a standalone tool and when displayed alongside search history.

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Section: Illustrative Example: Analyzing Structurementioning

confidence: 99%

Visualizations to Summarize Search Behavior

Howell

Choueiry

2020

Lecture Notes in Computer Science

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“…Quite recently, strong domain filtering consistencies have received attention [7,32]. Moreover, efficient ways to apply relational consistencies were proposed and new consistencies of this type were introduced for binary constraints [19,14,38] and non-binary constraints [16,37].…”

Section: Related Workmentioning

confidence: 99%

Strong local consistency algorithms for table constraints

Paparrizou¹,

Stergiou²

2015

Constraints

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Table constraints are important in constraint programming as they are present in many real problems from areas such as configuration and databases. As a result, numerous specialized algorithms that achieve generalized arc consistency (GAC) on table constraints have been proposed. Since these algorithms achieve GAC, they operate on one constraint at a time. In this paper we propose new filtering algorithms for positive table constraints that achieve stronger local consistency properties than GAC by exploiting intersections between constraints. The first algorithm, called maxRPWC+, is a domain filtering algorithm that is based on the local consistency maxRPWC and extends the GAC algorithm of Lecoutre and Szymanek [23]. The second algorithm extends the state-of-the-art STR-based algorithms to stronger relation filtering consistencies, i.e., consistencies that can remove tuples from constraints' relations. Experimental results from benchmark problems demonstrate that the proposed algorithms are quite competitive with standard GAC algorithms like STR2 in some classes of problems with intersecting table constraints, being orders of magnitude faster in some cases.

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“…This has led to the development of efficient solvers providing a rich modelling language. Stronger notions of consistency have been proposed for domain reduction which lead to more eliminations but at greater computational cost [1,2,31].…”

Section: Introductionmentioning

confidence: 99%

Strengthening neighbourhood substitution

Cooper¹

2020

Preprint

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Domain reduction is an essential tool for solving the constraint satisfaction problem (CSP). In the binary CSP, neighbourhood substitution consists in eliminating a value if there exists another value which can be substituted for it in each constraint. We show that the notion of neighbourhood substitution can be strengthened in two distinct ways without increasing time complexity. We also show the theoretical result that, unlike neighbourhood substitution, finding an optimal sequence of these new operations is NP-hard. ⋆ The author received funding from the French Investing for the Future PIA3 program under the Grant agreement ANR-19-PI3A-000, in the context of the ANITI project. if NSlist = ∅ then pop (p, u, v) from NSlist ; OK := (u, v ∈ D(xp)) ; else pop (p, u, q) from CNSlist ; OK := (u ∈ D(xp) ∧ Uncovered(p, u, q)) ; if OK then delete u fom D(xp) ; *** Update NbBlocks and propagate *** for all i such that {i, p} ∈ E : for all a, b ∈ D(xi) such that (b, u) ∈ Rip and (a, u) / ∈ Rip : ............(1) NbBlocks(i, b, a, p) := NbBlocks(i, b, a, p) −1 ; if NbBlocks(i, b, a, p) = 0 then BlockVars(i, b, a) := BlockVars(i, b, a) \{p} ; if BlockVars(i, b, a) becomes ∅ then *** NS *** add (i, b, a) to NSlist ; if BlockVars(i, b, a) becomes a singleton {j} then .

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Revisiting Neighborhood Inverse Consistency on Binary CSPs

Cited by 7 publications

References 14 publications

Visualizations to Summarize Search Behavior

Visualizations to Summarize Search Behavior

Strong local consistency algorithms for table constraints

Strengthening neighbourhood substitution

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