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This letter studies the problem of minimizing increasing set functions, orequivalently, maximizing decreasing set functions, over the base of a matroid.This setting has received great interest, since it generalizes several appliedproblems including actuator and sensor placement problems in control theory,multi-robot task allocation problems, video summarization, and many others. Westudy two greedy heuristics, namely, the forward and the reverse greedyalgorithms. We provide two novel performance guarantees for the approximatesolutions obtained by these heuristics depending on both the submodularityratio and the curvature.

Performance guarantees of forward and reverse greedy algorithms for minimizing nonsupermodular nonsubmodular functions on a matroid