An Approach of Solving Constraint Satisfaction Problem Based on Cycle-Cut

Abstract

Firstly a backtrack-free algorithm Tree_Search is given to solve the cycle-free CSPs. Secondly,by embedding the cycle-cut idea in the MAC3rm algorithm which is the most popular solver for binary CSPs in recent years,the new algorithm,called CCS,is presented.CCS separates the backtracking procedure into two steps,the former step searches the partial solution for the variables in the cycle-cut set and simplifies the problem into a cycle-free problem that is arc consistency,and the latter step solves the rest variables by Tree_Search algorithm.As a result, CCS has improved MAC3rm.It is proved that the partial solution which is found by MAC3rm can be extended to a global solution and MAC3rm can not find a partial solution on the cycle_cut set if the global solution does not exist.The experiments show that CCS is more efficient than MAC3rm.While solving the random CSPs which are at the phase transition,CCS can reach a maximum of 140 times more efficient than MAC3rm,and while solving some of the benchmarks, CCS can reach up to 100 times more efficient than MAC3rm.