PATH CONSISTENCY REVISITED
One of the main factors limiting the use of path consistency algorithms in real life applications is their high space complexity. Han and Lee proposed a path consistency algorithm, PC-4, with O(n3a3) space complexity, which makes it practicable only for small problems. I present 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 Bessiere) 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 a new support only if the current support is eliminated. I also show that PC-5 can be improved further to yield an algorithm, PC5++, with even better average-case performance and the same space complexity.