Path consistency revisited

One of the main factors limiting the use of path consistency algorithms in real life applications is their high space complexity. C. Han and C. Lee (1988) presented a path consistency algorithm, PC-4, with O(n³a³) space complexity, which makes it practicable only for small problems. The author presents a new path consistency algorithm, PC-5, which has an O(n³a²) space complexity while retaining the worst case time complexity of PC-4. Moreover, the new algorithm exhibits a much better average case time complexity. The new algorithm is based on the idea (due to C. Bessiere (1994)) that, at any time, only a minimal amount of support has to be found and recorded for a labeling to establish its viability; one has to look for at new support only if the current support is eliminated. The author also shows that PC-5 can be improved further to yield an algorithm, PC5++, with even better average case performance and the same space complexity