For a matroid M, Edmonds proved that its ground set contains k disjoint bases if and only if |A| >= k(r(E) -- r( ¯A)) for every subset A of the ground set E. Here r is the rank function of M. We study the system of inequalities x(A) >= k(r(E) -- r( ¯A)), 0 <= x <= u. We show that if u is integer valued then this defines a polyhedron with integer extreme points. We also show that this is a TDI system. We give a simple combinatorial algorithm for solving the associated optimization problem. Related results have been obtained by Frank & Tardos with the use of generalized polymatroids.
By: Francisco Barahona, Herve Kerivin
Published in: RC22634 in 2002
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .