The tight asymptotic approximation ratio of First Fit for bin packing with cardinality constraints

György Dósa, Leah Epstein

Research output: Contribution to journalArticlepeer-review

Abstract

In bin packing with cardinality constraints (BPCC), there is an upper bound k≥2 on the number of items that can be packed into each bin, additionally to the standard constraint on the total size of items. We study the algorithm First Fit (FF), acting on a list of items, packing each item into the minimum indexed bin that contains at most k−1 items and has sufficient space for the item. We present a complete analysis of its asymptotic approximation ratio for all values of k. Many years after FF for BPCC was introduced, its tight asymptotic approximation ratio is finally found.

Original languageEnglish
Pages (from-to)33-49
Number of pages17
JournalJournal of Computer and System Sciences
Volume96
DOIs
StatePublished - Sep 2018

Bibliographical note

Funding Information:
Gy. D?sa was supported by Szechenyi 2020 under the EFOP-3.6.1-16-2016-00015 and grant SNN 116095 ?National Research, Development and Innovation Office ? NKFIH?.

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

  • Asymptotic approximation ratio
  • Bin packing
  • First fit

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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