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

Kemin Yu (), Min Li (), Yang Zhou () and Qian Liu ()
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Kemin Yu: Shandong Normal University
Min Li: Shandong Normal University
Yang Zhou: Shandong Normal University
Qian Liu: Shandong Normal University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 3, No 11, 21 pages

Abstract: Abstract 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 $$\frac{1}{m+2}(1-e^{-(m+2)})$$ 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 $$\frac{1}{m+3}(1-e^{-(m+3)})$$ 1 m + 3 ( 1 - e - ( m + 3 ) ) .

Keywords: k-Submodularity; Knapsack constraint; Matroid constraint; Approximation algorithm; 90C27; 68W40; 68W25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01021-w

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