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The problem of maximizing a non-negative submodular function was introduced by Feige, Mirrokni, and Vondrak [FOCS'07] who provided a deterministic local-search based algorithm that guarantees an approximation ratio of 1 3 , as well as a randomized 2 5-approximation algorithm. An extensive line of research followed and various algorithms with improving… (More)
In this note we study the greedy algorithm for combinatorial auctions with submodular bidders. It is well known that this algorithm provides an approximation ratio of 2 for every order of the items. We show that if the valuations are vertex cover functions and the order is random then the expected approximation ratio imrpoves to 7 4 .