Post matching - a distributive analog of independent matching
- Univ. of Illinois, Chicago, IL (United States)
Poset matroids, also known as distributive supermatriods, were considered by Dunstan, Ingleton, Welsh and by Faigle. They generalize matroids to the context of posets, where instead of independent sets one has independent ideals. Significant examples of poset matroids include integral matroids, generalizing polymatroids, and transversal and matching poset matroids, generalizing transversal and matching matroids. Motivated by the desire to generalize matroid intersection in this direction, we consider a bipartite graph with a poset matroid on each side of it, such that the neighbors of any element form an ideal. A matching whose saturated elements form independent ideals is called a poset matching. This generalizes both matroid intersection and independent matching. We present a polynomial-time augmenting-path algorithm constructing a largest poset matching, and prove analogs of Koenig-Egervary, Rado, and Mendelsohn-Dulmage theorems. The algorithm can also evaluate the rank function of the Dilworth completion of a poset matroid. Finally, we show how to solve the weighted poset matching problem using a polynomial number of calls to the independence oracles of the two poset matroids.
- OSTI ID:
- 36379
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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