An Efficient Algorithm for Decomposition of Partially Ordered Sets

Abstract

Efficient time complexities for partial ordered sets or posets are well-researched field. Hopcroft and Karp introduced an algorithm that solves the minimal chain decomposition in O (n2.5) time. Felsner et al. proposed an algorithm that reduces the time complexity to O (kn2) such that n is the number of elements of the poset and k is its width. The main goal of this paper is proposing an efficient algorithm to compute the width of a given partially ordered set P according to Dilworth’s theorem. It is an efficient and simple algorithm. The time complexity of this algorithm is O (kn), such that n is the number of elements of the partially ordered set P and k is the width of P. The computational results show that the proposed algorithm outperforms other related algorithms.