Improving the Performance of Consistency Algorithms by Localizing and Bolstering Propagation in a Tree Decomposition

Abstract

The tractability of a Constraint Satisfaction Problem (CSP)is guaranteed by a direct relationship between its consistencylevel and a structural parameter of its constraint network suchas the treewidth. This result is not widely exploited in practicebecause enforcing higher-level consistencies can be costlyand can change the structure of the constraint network andincrease its width. Recently, R(*,m)C was proposed as a relational consistency property that does not modify the structureof the graph and, thus, does not affect its width. In this paper,we explore two main strategies, based on a tree decomposition of the CSP, for improving the performance of enforcingR(*,m)C and getting closer to the above tractability condition. Those strategies are: a) localizing the application ofthe consistency algorithm to the clusters of the tree decomposition, and b) bolstering constraint propagation betweenclusters by adding redundant constraints at their separators,for which we propose three new schemes. We characterizethe resulting consistency properties by comparing them, theoretically and empirically, to the original R(*,m)C and thepopular GAC and maxRPWC, and establish the benefits ofour approach for solving difficult problems.

Characterizing Performance of Consistency Algorithms by Algorithm Configuration of Random CSP Generators

“…2012) and solving difficult CSPs with higher levels of consistency (Karakashian, Woodward, and Choueiry 2013). In particular, we are interested in applying AllSol and PerTuple locally to the clusters of a tree decomposition (Geschwender et al 2013).…”

Selecting the Appropriate Consistency Algorithm for CSPs Using Machine Learning Classifiers

“…Each cluster is a subproblem that is treated as an independent CSP instance. This decomposition is performed because it corresponds to the intended use of the two algorithms (Karakashian, Woodward, and Choueiry 2013). We ran both AllSol and PerTuple on every subproblem and recorded their run times.…”

“…One such important consistency property is constraint minimality, which guarantees that every tuple in a constraint definition appears in a solution to the CSP (Montanari 1974). This property was shown to be important for knowledge compilation (Gottlob 2012) and achieving higher consistency levels (Karakashian, Woodward, and Choueiry 2013). Karakashian et al proposed two algorithms, PerTuple and AllSol, for computing the minimal network (2012).…”