2026-07-25T21:33:26Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14111 2024-03-06T10:53:30Z ddc:004 open_access

Additive Approximation Schemes for Load Balancing Problems Buchem, Moritz Rohwedder, Lars Vredeveld, Tjark Wiese, Andreas Load balancing Approximation schemes Parallel machine scheduling We formalize the concept of additive approximation schemes and apply it to load balancing problems on identical machines. Additive approximation schemes compute a solution with an absolute error in the objective of at most ε h for some suitable parameter h and any given ε > 0. We consider the problem of assigning jobs to identical machines with respect to common load balancing objectives like makespan minimization, the Santa Claus problem (on identical machines), and the envy-minimizing Santa Claus problem. For these settings we present additive approximation schemes for h = p_{max}, the maximum processing time of the jobs. Our technical contribution is two-fold. First, we introduce a new relaxation based on integrally assigning slots to machines and fractionally assigning jobs to the slots. We refer to this relaxation as the slot-MILP. While it has a linear number of integral variables, we identify structural properties of (near-)optimal solutions, which allow us to compute those in polynomial time. The second technical contribution is a local-search algorithm which rounds any given solution to the slot-MILP, introducing an additive error on the machine loads of at most ε⋅ p_{max}. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Moritz Buchem and Lars Rohwedder and Tjark Vredeveld and Andreas Wiese 2021 Is Part Of LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2021.42 urn:nbn:de:0030-drops-141116 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.42 eng https://creativecommons.org/licenses/by/4.0/legalcode