Optimal matroid bases with intersection constraints: valuated matroids, M-convex functions, and their applications

For two matroids M 1 and M 2 with the same ground set V and two cost functions w 1 and w 2 on 2 V , we consider the problem of finding bases X 1 of M 1 and X 2 of M 2 minimizing w 1 ( X 1 ) + w 2 ( X 2 ) subject to a certain cardinality constraint on their intersection X 1 ∩ X 2 . For this problem,...

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