On maximizing monotone or non-monotone k-submodular functions with the intersection of knapsack and matroid constraints

A k -submodular function is a generalization of a submodular function. The definition domain of a k -submodular function is a collection of k -disjoint subsets instead of simple subsets of ground set. In this paper, we consider the maximization of a k -submodular function with the intersection of a...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 45; no. 3; p. 93
Main Authors: Yu, Kemin, Li, Min, Zhou, Yang, Liu, Qian
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2023
Springer Nature B.V
Subjects:
Algorithms
Approximation
Combinatorics
Constraints
Convex and Discrete Geometry
Greedy algorithms
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Maximization
Operations Research/Decision Theory
Optimization
S.I. : AAIM 2022
Search algorithms
Theory of Computation
68W40
Matroid constraint
Submodularity
90C27
68W25
Approximation algorithm
Knapsack constraint
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:A k -submodular function is a generalization of a submodular function. The definition domain of a k -submodular function is a collection of k -disjoint subsets instead of simple subsets of ground set. In this paper, we consider the maximization of a k -submodular function with the intersection of a knapsack and m matroid constraints. When the k -submodular function is monotone, we use a special analytical method to get an approximation ratio 1 m + 2 ( 1 - e - ( m + 2 ) ) for a nested greedy and local search algorithm. For non-monotone case, we can obtain an approximate ratio 1 m + 3 ( 1 - e - ( m + 3 ) ) .
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-023-01021-w