@inproceedings{b7bf7db9350840378567d216d20cd58d,
title = "An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding",
abstract = "We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in [0, 1], and a partition matroid over the items. The goal is to pack the items in a minimum number of unit-size bins, such that each bin forms an independent set in the matroid. This variant of classic Bin Packing has natural applications in secure storage on the Cloud, as well as in equitable scheduling and clustering with fairness constraints. Our main result is an asymptotic fully polynomial-time approximation scheme (AFPTAS) for Bin Packing with a partition matroid constraint. This scheme generalizes the known AFPTAS for Bin Packing with Cardinality Constraints and improves the existing asymptotic polynomial-time approximation scheme (APTAS) for Group Bin Packing, which are both special cases of Bin Packing with partition matroid. We derive the scheme via a new method for rounding a (fractional) solution for a configuration-LP. Our method uses this solution to obtain prototypes, in which items are interpreted as placeholders for other items, and applies fractional grouping to modify a fractional solution (prototype) into one having desired integrality properties.",
keywords = "AFPTAS, bin packing, LP-rounding, partition-matroid",
author = "Ilan Doron-Arad and Ariel Kulik and Hadas Shachnai",
note = "Publisher Copyright: {\textcopyright} 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.; 26th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2023 and the 27th International Conference on Randomization and Computation, RANDOM 2023 ; Conference date: 11-09-2023 Through 13-09-2023",
year = "2023",
month = sep,
day = "1",
doi = "10.4230/LIPIcs.APPROX/RANDOM.2023.22",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Nicole Megow and Adam Smith",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2023",
address = "Germany",
}