An almost optimal approximation algorithm for monotone submodular multiple knapsack

We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint. The input is a set I of items, each has a non-negative weight, and a set of bins of arbitrary capacities. Also, we are given a submodular, monotone and non-negative function f over subsets of...

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Veröffentlicht in:Journal of computer and system sciences Jg. 125; S. 149 - 165
Hauptverfasser: Fairstein, Yaron, Kulik, Ariel, Naor, Joseph (Seffi), Raz, Danny, Shachnai, Hadas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.05.2022
Schlagworte:
Approximation algorithms
Monotone submodular functions
Multiple Knapsack constraint
Approximation algorithms
Monotone submodular functions
Multiple Knapsack constraint
ISSN:0022-0000, 1090-2724
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Zusammenfassung:We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint. The input is a set I of items, each has a non-negative weight, and a set of bins of arbitrary capacities. Also, we are given a submodular, monotone and non-negative function f over subsets of the items. The objective is to find a packing of a subset of items A⊆I in the bins such that f(A) is maximized. Our main result is an almost optimal polynomial time (1−e−1−ε)-approximation algorithm for the problem, for any ε>0. The algorithm relies on a structuring technique which converts a general multiple knapsack constraint to a constraint in which the bins are partitioned into groups of exponentially increasing cardinalities, each consisting of bins of uniform capacity. We derive the result by combining structuring with a refined analysis of techniques for submodular optimization subject to knapsack constraints.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2021.11.005