Matching is a classic problem with a rich history and a significant impact, both on the theory
of algorithms and in practice. Recently there has been a surge of interest in the online …

Let f:2^X→\calR_+ be a monotone submodular set function, and let (X,\calI) be a matroid.
We consider the problem \rmmax_S∈\calIf(S). It is known that the greedy algorithm yields a …

A number of recent results on optimization problems involving submodular functions have
made use of the multilinear relaxation of the problem. These results hold typically in the …

We study the problem of approximating maximum Nash social welfare (NSW) when
allocating m indivisible items among n asymmetric agents with submodular valuations. The …

2^{X}\rightarrow\mathcal {R}+\mathrm {b}\mathrm {e} a monotone submodular function. The
curvature of f is the minimum c\in [0, 1] such that for any S\subset X and j\in X\backslash S, f …

We prove that no online algorithm (even randomized, against an oblivious adversary) is
better than 1/2-competitive for welfare maximization with coverage valuations, unless NP …

We consider the problem of approximating maximum Nash social welfare (NSW) while
allocating a set of indivisible items to n agents. The NSW is a popular objective that provides …

Applications in complex systems such as the Internet have spawned a recent interest in
studying situations involving multiple agents with their individual cost or utility functions. In …

We consider the Submodular Welfare Problem where we have m items and n players with
given utility functions wi: 2 [m]→ R+. The utility functions are assumed to be monotone and …

Multiagent resource allocation provides mechanisms to allocate bundles of resources to
agents, where resources are assumed to be indivisible and nonshareable. A central goal is …