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Maximizing a Monotone Submodular Function Subject to a Matroid Constraint

- G. Calinescu, C. Chekuri, M. Pál, J. Vondrák
- Mathematics, Computer Science
- SIAM J. Comput.
- 1 November 2011

An improved coating pan apparatus and spray arm assembly are disclosed for providing facilitated maintenance and cleaning of sensitive spray nozzles. The spray arm assembly includes means for varying… Expand

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

- J. Vondrák
- Computer Science, Mathematics
- STOC '08
- 17 May 2008

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… Expand

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

- G. Calinescu, C. Chekuri, M. Pál, J. Vondrák
- Computer Science, Mathematics
- IPCO
- 25 June 2007

Let $f:2^{N} \rightarrow \cal R^{+}$ be a non-decreasing submodular set function, and let $(N,\cal I)$ be a matroid. We consider the problem $\max_{S \in \cal I} f(S)$. It is known that the greedy… Expand

Fast algorithms for maximizing submodular functions

- Ashwinkumar Badanidiyuru, J. Vondrák
- Computer Science, Mathematics
- SODA
- 5 January 2014

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… Expand

Maximizing Non-monotone Submodular Functions

- U. Feige, V. Mirrokni, J. Vondrák
- Computer Science, Mathematics
- SIAM J. Comput.
- 1 July 2011

Submodular maximization generalizes many important problems including Max Cut in directed and undirected graphs and hypergraphs, certain constraint satisfaction problems, and maximum facility… Expand

Submodular maximization by simulated annealing

- Shayan Oveis Gharan, J. Vondrák
- Computer Science, Mathematics
- SODA '11
- 9 July 2010

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… Expand

Lazier Than Lazy Greedy

- Baharan Mirzasoleiman, Ashwinkumar Badanidiyuru, Amin Karbasi, J. Vondrák, Andreas Krause
- Computer Science, Mathematics
- AAAI
- 28 September 2014

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

Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures

- C. Chekuri, J. Vondrák, R. Zenklusen
- Mathematics, Computer Science
- IEEE 51st Annual Symposium on Foundations of…
- 23 October 2010

We consider the problem of randomly rounding a fractional solution $x$ in an integer polytope $P \subseteq [0,1]^n$ to a vertex $X$ of $P$, so that $\E[X] = x$. Our goal is to achieve {\em… Expand

Maximizing Non-Monotone Submodular Functions

- U. Feige, V. Mirrokni, J. Vondrák
- Computer Science
- 48th Annual IEEE Symposium on Foundations of…
- 2007

Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location… Expand

Submodular function maximization via the multilinear relaxation and contention resolution schemes

- C. Chekuri, J. Vondrák, R. Zenklusen
- Computer Science, Mathematics
- STOC '11
- 23 May 2011

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,… Expand