Abstract
Given a digraph G = (VG,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 Geelen 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; its running time is O(n 4) (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 3 logn)-time algorithm for finding a maximum cardinality even factor in an odd-cycle symmetric digraph. This technique also applies to a wide variety of related problems.
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Babenko, M.A. (2010). A Faster Algorithm for the Maximum Even Factor Problem. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17517-6_40
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DOI: https://doi.org/10.1007/978-3-642-17517-6_40
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