Extended analysis of intelligent backtracking algorithms for the maximal constraint satisfaction problem

Overconstrained systems refer to sets of soft constraints which do not permit a solution satisfying all the constraints. The overconstrainedness in such soft-constraint systems can be manifested in a wide variety of structures, including weighted constraints, partially ordered constraints, constraint hierarchies and references. The simplest among these formalisms is the maximal constraint satisfaction problem (CSP), where a solution is sought which satisfies the maximum number of constraints. In this paper, backtracking algorithms and their intelligent versions used in the ordinary CSP context, are studied in context of the maximal CSP. The algorithms of E.C. Freuder and R.J. Wallace (1995) for depth-first branch-and-bound and backjumping are extended to conflict-directed backjumping. A theoretical analysis of the problem of application of intelligent backtracking algorithms for maximal CSP is provided.