Computing Minimum Directed Feedback Vertex Set in O(1.9977n)

Abstract

In this paper we propose an algorithm which, given a directed graph G, finds the minimum directed feedback vertex set (FVS) of G in O∗(1.9977n) time and polynomial space. To the best of our knowledge, this is the first algorithm computing the minimum directed FVS faster than in O(2n). The algorithm is based on the branch-and-prune principle. The minimum directed FVS is obtained through computing of the complement, i.e. the maximum induced directed acyclic graph. To evaluate the time complexity, we use the measureand-conquer strategy according to which the vertices are assigned with weights and the size of the problem is measured in the sum of weights of vertices of the given graph rather than in the number of the vertices.