Fast algorithms for maximizing monotone nonsubmodular functions

In recent years, with the more and more researchers studying the problem of maximizing monotone (nonsubmodular) objective functions, the approximation algorithms for this problem have gotten much progress by using some interesting techniques. In this paper, we develop the approximation algorithms fo...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 43; no. 5; pp. 1655 - 1670
Main Authors: Liu, Bin, Hu, Miaomiao
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2022
Springer Nature B.V
Subjects:
Approximation
Combinatorics
Convex and Discrete Geometry
Greedy algorithms
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Maximization
Operations Research/Decision Theory
Optimization
Queries
Theory of Computation
Nonsubmodular Function
Matroid constraint
Approximation algorithm
Cardinality constraint
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:In recent years, with the more and more researchers studying the problem of maximizing monotone (nonsubmodular) objective functions, the approximation algorithms for this problem have gotten much progress by using some interesting techniques. In this paper, we develop the approximation algorithms for maximizing a monotone function f with generic submodularity ratio γ subject to certain constraints. Our first result is a simple algorithm that gives a ( 1 - e - γ - ϵ ) -approximation for a cardinality constraint using O ( n ϵ l o g n ϵ ) queries to the function value oracle. The second result is a new variant of the continuous greedy algorithm for a matroid constraint. We combine the variant of continuous greedy method with the contention resolution schemes to find a solution with approximation ratio ( γ 2 ( 1 - 1 e ) 2 - O ( ϵ ) ) , and the algorithm makes O ( r n ϵ - 4 l o g 2 n ϵ ) queries to the function value oracle.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-021-00717-1