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 .
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)