Faster Muse Csp Arc Consistency Algorithms

MUSE CSP (MU ltiply SEgmented Constraint Satisfaction Problem) [5, 6] is an extension to the constraint satisfaction problem (CSP) which is especially useful for problems that segment into multiple instances of CSP that share variables. In Helzerman and Harper [6], the concepts of MUSE node, arc, and path consistency were de ned and algorithms for MUSE arc consistency, MUSE AC-1, and MUSE path consistency were developed. MUSE AC-1 is similar to the CSP arc consistency algorithm AC-4 [11]. Recently, Bessi ere developed a new algorithm, AC-6 [1], which has the same worst-case running time as AC-4 and is faster than AC-3 and AC-4 in practice. In this paper, we focus on developing two faster MUSE arc consistency algorithms: MUSE AC-2, which directly applies Bessi ere's method to improve upon MUSE AC-1, and MUSE AC-3, which uses our new \lazy" evaluation method for keeping track of the additional sets required by the MUSE approach. These new algorithms decrease the number of steps required to achieve arc consistency in randomly generated MUSE CSP instances when compared to MUSE AC-1.