Experimental Evaluation of Branching Schemes for the CSP

The search strategy of a CP solver is determined by the variable and value ordering heuristics it employs and by the branching scheme it follows. Although the effects of variable and value ordering heuristics on search effort have been widely studied, the effects of different branching schemes have received less attention. In this paper we study this effect through an experimental evaluation that includes standard branching schemes such as 2-way, d-way, and dichotomic domain splitting, as well as variations of set branching where branching is performed on sets of values. We also propose and evaluate a generic approach to set branching where the partition of a domain into sets is created using the scores assigned to values by a value ordering heuristic, and a clustering algorithm from machine learning. Experimental results demonstrate that although exponential differences between branching schemes, as predicted in theory between 2-way and d-way branching, are not very common, still the choice of branching scheme can make quite a difference on certain classes of problems. Set branching methods are very competitive with 2-way branching and outperform it on some problem classes. A statistical analysis of the results reveals that our generic clustering-based set branching method is the best among the methods compared.Comment: To appear in the 3rd workshop on techniques for implementing constraint programming systems (TRICS workshop at the 16th CP Conference), St. Andrews, Scotland 201

A Partial Taxonomy of Substitutability and Interchangeability

Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the different concepts, and indicate directions for future work, in particular with respect to making connections with research into symmetry breaking. This paper is a condensed version of a larger work in progress.Comment: 18 pages, The 10th International Workshop on Symmetry in Constraint Satisfaction Problems (SymCon'10