2026-08-10T22:35:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18751 2024-03-06T11:02:38Z ddc:004 open_access

Simple Deterministic Approximation for Submodular Multiple Knapsack Problem Sun, Xiaoming Zhang, Jialin Zhang, Zhijie Submodular maximization knapsack problem deterministic algorithm 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]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Xiaoming Sun and Jialin Zhang and Zhijie Zhang 2023 Is Part Of LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2023.98 urn:nbn:de:0030-drops-187517 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.98 eng https://creativecommons.org/licenses/by/4.0/legalcode