An algorithm for packing non-zero A-paths in group-labelled graphs

Authors:
Maria Chudnovsky;William H. Cunningham;Jim Geelen
Affiliations:
Department of Industrial Engineering and Operations Research, Columbia University, New York, USA 10027;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada N2L 3G1;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada N2L 3G1
Venue:
Combinatorica
Year:
2008

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Abstract

Let G = (V, E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A 驴 V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We give an efficient algorithm for finding a maximum collection of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem.