Matching Problems in Polymatroids Without Double Circuits

According to the present state of the theory of the matroid matching problem, the existence of a good characterization to the size of a maximum matching depends on the behavior of certain substructures, called double circuits. In this paper we prove that if a polymatroid has no double circuits at all, then a partition-type min-max formula characterizes the size of a maximum matching. We provide applications of this result to parity constrained orientations and to a rigidity problem. A polynomial time algorithm is constructed by generalizing the principle of shrinking blossoms used in Edmonds’ matching algorithm [2].

• Type: Conference
• Year: 2007
• Where: IPCO
• Authors: Márton Makai, Gyula Pap, Jácint Szabó
• Keywords: Double Circuits, IPCO 2007, Matroid Matching Problem, Maximum Matching, Optimization