In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2[m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that… (More)

Let f : 2 → R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2approximation [17] for this… (More)

Let f : 2 → R be a non-decreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2-approximation [9] for… (More)

We consider the problem of maximizing a non-negative submodular set function f:2N -> RR+ over a ground set N subject to a variety of packing type constraints including (multiple) matroid constraints,… (More)

We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [9] showed a 2/5-approximation for the unconstrained… (More)

There has been much progress recently on improved approximations for problems involving submodular objective functions, and many interesting techniques have been developed. However, the resulting… (More)

2006 47th Annual IEEE Symposium on Foundations of…

2006

Combinatorial allocation problems require allocating items to players in a way that maximizes the total utility. Two such problems received attention recently, and were addressed using the same… (More)

Is it possible to maximize a monotone submodular function faster than the widely used lazy greedy algorithm (also know n as accelerated greedy), both in theory and practice? In this paper, we develop… (More)