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Simple Deterministic Approximation for Submodular Multiple Knapsack Problem

Authors Xiaoming Sun, Jialin Zhang, Zhijie Zhang

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Author Details

Xiaoming Sun
  • Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China
  • University of Chinese Academy of Sciences, Beijing, China
Jialin Zhang
  • Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China
  • University of Chinese Academy of Sciences, Beijing, China
Zhijie Zhang
  • Center for Applied Mathematics of Fujian Province, School of Mathematics and Statistics, Fuzhou University, China

Funding

This work was supported in part by the National Natural Science Foundation of China Grants No. 61832003, 62272441.

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Xiaoming Sun, Jialin Zhang, and Zhijie Zhang. Simple Deterministic Approximation for Submodular Multiple Knapsack Problem. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 98:1-98:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ESA.2023.98

Abstract

Submodular maximization has been a central topic in theoretical computer science and combinatorial optimization over the last decades. Plenty of well-performed approximation algorithms have been designed for the problem over a variety of constraints. In this paper, we consider the submodular multiple knapsack problem (SMKP). In SMKP, the profits of each subset of elements are specified by a monotone submodular function. The goal is to find a feasible packing of elements over multiple bins (knapsacks) to maximize the profit. Recently, Fairstein et al. [ESA20] proposed a nearly optimal (1-e^{-1}-ε)-approximation algorithm for SMKP. Their algorithm is obtained by combining configuration LP, a grouping technique for bin packing, and the continuous greedy algorithm for submodular maximization. As a result, the algorithm is somewhat sophisticated and inherently randomized. In this paper, we present an arguably simple deterministic combinatorial algorithm for SMKP, which achieves a (1-e^{-1}-ε)-approximation ratio. Our algorithm is based on very different ideas compared with Fairstein et al. [ESA20].

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Submodular maximization
  • knapsack problem
  • deterministic algorithm

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