2026-09-08T02:21:24Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26449 2026-09-05T19:44:09Z ddc:004 open_access

Near-Tight Approximation Algorithms for Bottleneck Multiple Knapsack Problems Chen, Lin Hu, Tingwei Mao, Yuchen Chen, Yong Mei, Lili Zhang, An Chen, Guangting Zhang, Guochuan Bottleneck multiple knapsack approximation algorithms In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the minimum profit received by any knapsack subject to the capacity constraint. When all knapsacks have identical capacity, we give a (2/3 - ε)-approximation algorithm for any constant ε > 0. This result almost matches the (2/3 + ε) inapproximability bound for the bottleneck multiple subset sum problem (Caprara et al., 2000). When the knapsacks can have arbitrary capacities, we propose a (1/2 - ε)-approximation algorithm for any constant ε > 0. We also prove a hardness bound of (1/2 + ε) for any constant ε > 0. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Lin Chen and Tingwei Hu and Yuchen Mao and Yong Chen and Lili Mei and An Zhang and Guangting Chen and Guochuan Zhang 2026 Is Part Of LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2026.60 urn:nbn:de:0030-drops-264495 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.60 eng https://creativecommons.org/licenses/by/4.0/legalcode