A Faster Algorithm for the Maximum Even Factor Problem

Given a digraph G = (V G,AG), an even factor M ⊆ AG is a subset of arcs that decomposes into a collection of node-disjoint paths and even cycles. Even factors in digraphs were introduced by Geleen and Cunningham and generalize path matchings in undirected graphs. Finding an even factor of maximum cardinality in a general digraph is known to be NP-hard but for the class of odd-cycle symmetric digraphs the problem is polynomially solvable. So far, the only combinatorial algorithm known for this task is due to Pap; it has the running time of O(n) (hereinafter n stands for the number of nodes in G). In this paper we present a novel sparse recovery technique and devise an O(n log n)-time algorithm for finding a maximum cardinality even factor in an odd-cycle symmetric digraph.