Jan Vondrák

Maximizing Non-monotone Submodular Functions

Submodular maximization generalizes many important problems including Max Cut in directed and undirected graphs and hypergraphs, certain constraint satisfaction problems, and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular functions is NP-hard. In this paper, we design the first constant-factor approximation algorithms for maximizing nonnegative (non-monotone) submodular functions. In particular, we give a deterministic local-search

Optimal approximation for the submodular welfare problem in the value oracle model

frac{1}{3}

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint

-approximation and a randomized

Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e

frac{2}{5}

Maximizing Non-Monotone Submodular Functions

-approximation algorithm for maximizing nonnegative submodular functions. We also show that a uniformly random set gives a

Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)

frac{1}{4}

Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures

-approximation. For symmetric submodular functions, we show that a random set gives a

Submodular function maximization via the multilinear relaxation and contention resolution schemes

frac{1}{2}

Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions

-approximation, which can also be achieved by deterministic local search. These algorithms work in the value oracle model, where the submodular function is accessible through a black box returning

Submodular Maximization over Multiple Matroids via Generalized Exchange Properties

f(S)