Matroidal Approximations of Independence Systems
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Milgrom (2017) has proposed a heuristic for determining a maximum weight basis of an independence system I given that for sets from O ⊆ I we care in particular about the qualitiy of approximation as we assume, that O contains (frequently) the optimal basis. It is based on finding an `inner matroid', one contained in the independence system. We show that without additional assumptions on O being different from I the worst-case performance of this new heuristic is no better than that of the classical greedy algorithm.
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