Computing the Frequency of Partial Orders

Abstract. In this paper we study four algorithms for computing the frequency of a given partial order. Here the frequency of a partial order is the number of standard labellings respecting that partial order. The first two algorithms count by enumerating all solutions to a CSP. However, large numbers of solutions to CSPs soon make algorithms based on enumeration infeasible. The third and fourth algorithm, to a degree, overcome this problem. They avoid repeatedly solving problems with certain kinds of isomorphic solutions. A prototype implementation of the fourth algorithm was significantly more efficient than an enumeration based counting implementation using OPL.