Year: 2016
Type: preprint
Abstract: The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining further improvements for many submodular maximization problems boils down to finding better algorithms for optimizing a relaxation of them known as the multilinear extension. In this work we present an algorithm for optimizing the multilinear relaxation whose guarantee improves over the guarantee of the best previous algorithm (which was given by Ene and Nguyen (2016)). Moreover, our algorithm is based on a new technique which is, arguably, simpler and more natural for the problem at hand. In a nutshell, previous algorithms for this problem rely on symmetry properties which are natural only in the absence of a constraint. Our technique avoids the need to resort to such properties, and thus, seems to be a better fit for constrained problems.
Source: arXiv (Cornell University)
Authors: Buchbinder, Niv, Feldman, Moran
Institutions: Tel Aviv University, Open University of Israel
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951079895