Applying decomposition methods to crossword puzzle problems

Abstract

Structural decomposition methods have been proposed for identifying tractable Constraint Satisfaction Problems (CSPs) [1-5]. The basic principle is to decompose a CSP into tree-structured sub-problems. The subproblems are solved independently, then the original CSP is solved in a backtrack-free manner after the tree structure is made arc-consistent, as described in [1]. In [5], we proposed four decomposition methods: HINGE+, CUT, TRAVERSE, and CaT and tested these methods on randomly generated CSPs. We compare these techniques on instances of the fully interlocked Crossword Puzzle Problems (CPPs) [6] taken from a public library [7] and identify special cases of the constraint hypergraphs where some decomposition techniques yield better results than others although in general the opposite holds. Our future work includes: 1) Identifying more such configurations, and building hybrid decompositions techniques that exploit this information; 2) Tailoring existing decomposition methods for fully interlocked CPPs so that every sub-problem, after backtrack search, has few solutions; and 3) Designing a heuristic for applying local search for fully interlocked CPPs. This work is supported by CAREER Award #0133568 from the National Science Foundation. © Springer-Verlag Berlin Heidelberg 2005.