2026-07-24T05:16:02Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17171 2024-03-06T10:59:09Z ddc:004 open_access

Maximizing a Submodular Function with Bounded Curvature Under an Unknown Knapsack Constraint Klimm, Max Knaack, Martin submodular function knapsack approximation algorithm robust optimization This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness factor of a policy is the worst case ratio of the solution obtained by following the policy and an optimal solution that knows the knapsack capacity. We develop an algorithm with a robustness factor that is decreasing in the curvature c of the submodular function. For the extreme cases c = 0 corresponding to a modular objective, it matches a previously known and best possible robustness factor of 1/2. For the other extreme case of c = 1 it yields a robustness factor of ≈ 0.35 improving over the best previously known robustness factor of ≈ 0.06. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Max Klimm and Martin Knaack 2022 Is Part Of LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2022.49 urn:nbn:de:0030-drops-171711 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.49 eng https://creativecommons.org/licenses/by/4.0/legalcode