A Generalization of Edmonds’ Matching and Matroid Intersection Algorithms

Abstract

The independent path-matching problem is a common generalization of the matching problem and the matroid intersection problem. Cunningham and Geelen proved that this problem is solvable in polynomial time via the ellipsoid method. We present a polynomial-time combinatorial algorithm for its unweighted version that generalizes the known combinatorial algorithms for the cardinality matching problem and the matroid intersection problem.