An Optimal Algorithm to Find the Jump Number of Partially Ordered Sets

The jump number of a partially ordered set (poset) P isthe minimum number of incomparable adjacent pairs (jumps) in some linearextension of P. The problem of finding a linear extension of Pwith minimum number of jumps (jump number problem) is known to beNP-hard in general and, at the best of our knowledge, no exactalgorithm for general posets has been developed. In this paper, wegive examples of applications of this problem and propose for thegeneral case a new heuristic algorithm and an exactalgorithm. Performances of both algorithms are experimentallyevaluated on a set of randomly generated test problems.