Post matching - a distributive analog of independent matching
Conference
·
OSTI ID:36379
- 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
Similar Records
Polymatroids and electrical networks
Learning binary matroid ports
Quantum Matching Theory (with new complexity-theoretic, combinatorial and topical insights on the nature of the quantum entanglement)
Conference
·
Fri Dec 30 23:00:00 EST 1994
·
OSTI ID:36329
Learning binary matroid ports
Conference
·
Fri Dec 30 23:00:00 EST 1994
·
OSTI ID:35922
Quantum Matching Theory (with new complexity-theoretic, combinatorial and topical insights on the nature of the quantum entanglement)
Conference
·
Mon Dec 31 23:00:00 EST 2001
·
OSTI ID:976109