The Library
Maximizing nonmonotone submodular functions under matroid or knapsack constraints
Tools
Lee, Jon, Mirrokni, Vahab S., Nagarajan, Viswanath and Sviridenko, Maxim (2010) Maximizing nonmonotone submodular functions under matroid or knapsack constraints. SIAM Journal on Discrete Mathematics, Vol.23 (No.4). pp. 2053-2078. doi:10.1137/090750020 ISSN 0895-4801.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1137/090750020
Abstract
Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Unlike submodular minimization, submodular maximization is NP-hard. In this paper, we give the first constant-factor approximation algorithm for maximizing any nonnegative submodular function subject to multiple matroid or knapsack constraints. We emphasize that our results are for nonmonotone submodular functions. In particular, for any constant $k$, we present a $(\frac{1}{k+2+\frac{1}{k}+\epsilon})$-approximation for the submodular maximization problem under $k$ matroid constraints, and a $(\frac{1}{5}-\epsilon)$-approximation algorithm for this problem subject to $k$ knapsack constraints ($\epsilon>0$ is any constant). We improve the approximation guarantee of our algorithm to $\frac{1}{k+1+\frac{1}{k-1}+\epsilon}$ for $k\geq2$ partition matroid constraints. This idea also gives a $(\frac{1}{k+\epsilon})$-approximation for maximizing a monotone submodular function subject to $k\geq2$ partition matroids, which is an improvement over the previously best known guarantee of $\frac{1}{k+1}$.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Journal or Publication Title: | SIAM Journal on Discrete Mathematics | ||||
Publisher: | Society for Industrial and Applied Mathematics | ||||
ISSN: | 0895-4801 | ||||
Official Date: | 2010 | ||||
Dates: |
|
||||
Volume: | Vol.23 | ||||
Number: | No.4 | ||||
Page Range: | pp. 2053-2078 | ||||
DOI: | 10.1137/090750020 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |