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Maximizing monotone submodular functions over the integer lattice.
- Source :
- Mathematical Programming; Nov2018, Vol. 172 Issue 1/2, p539-563, 25p
- Publication Year :
- 2018
-
Abstract
- The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose that a non-negative monotone submodular function f:Z+n→R+ is given via an evaluation oracle. Assume further that f satisfies the diminishing return property, which is not an immediate consequence of submodularity when the domain is the integer lattice. Given this, we design polynomial-time (1-1/e-ϵ)-approximation algorithms for a cardinality constraint, a polymatroid constraint, and a knapsack constraint. For a cardinality constraint, we also provide a (1-1/e-ϵ)-approximation algorithm with slightly worse time complexity that does not rely on the diminishing return property. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICAL functions
ALGORITHMS
VECTORS (Calculus)
ALGEBRA
MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 172
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 132480743
- Full Text :
- https://doi.org/10.1007/s10107-018-1324-y