Persistency in combinatorial optimization problems on matroids ?
Optimization problems on matroids are generalizations of such important combinatorial optimization problems like the problem of minimum spanning tree of a graph, the bipartite matching problem, flow problems, etc. We analyze algorithms for finding the maximum weight independent set of a matroid and for finding a maximum cardinality intersection of two matroids and extend them to obtain the so-called persistency partition of the basic set of the matroid, where contain elements belonging to all optimum solutions; contain elements not belonging to any optimum solution; contain elements that belong to some but not to all optimum solutions.
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