Exact and Heuristic Algorithms for the Jump Number Problem

The jump number problem consists in determining a linear extension, of a partially ordered set (poset), with minimum number of jumps. The problem is known to be NP-hard for generical posets. In the paper we present an exact algorithm based on dynamic programming, and a heuristic algorithm for the jump number problem for general posets. Performance analysis of both algorithms are performed on a number of randomly generated partially ordered sets.