Optimal Matroid Partitioning Problems
نویسندگان
چکیده
This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set E and k weighted matroids (E, Ii, wi), i = 1, . . . , k, and our task is to find a minimum partition (I1, . . . , Ik) of E such that Ii ∈ Ii for all i. For each objective function, we give a polynomial-time algorithm or prove NP-hardness. In particular, for the case when the given weighted matroids are identical and the objective function is the sum of the maximum weight in each set (i.e., ∑ k i=1 maxe∈Ii wi(e)), we show that the problem is strongly NP-hard but admits a PTAS.
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تاریخ انتشار 2017