Optimal analysis of best fit bin packing

György Dósa, Jiří Sgall

Research output: Chapter in Book/Report/Conference proceedingConference contribution

19 Citations (Scopus)

Abstract

In early seventies it was shown that the asymptotic approximation ratio of BestFit bin packing is equal to 1.7. We prove that also the absolute approximation ratio for BestFit bin packing is exactly 1.7, improving the previous bound of 1.75. This means that if the optimum needs Opt bins, BestFit always uses at most ⌊1.7·OPT⌋ bins. Furthermore we show matching lower bounds for all values of Opt, i.e., we give instances on which BestFit uses exactly ⌊1.7·OPT⌋ bins. Thus we completely settle the worst-case complexity of BestFit bin packing after more than 40 years of its study.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages429-441
Number of pages13
Volume8572 LNCS
EditionPART 1
ISBN (Print)9783662439470
DOIs
Publication statusPublished - 2014
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: Jul 8 2014Jul 11 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8572 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other41st International Colloquium on Automata, Languages, and Programming, ICALP 2014
CountryDenmark
CityCopenhagen
Period7/8/147/11/14

Fingerprint

Bin Packing
Bins
Asymptotic Approximation
Lower bound
Approximation

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Dósa, G., & Sgall, J. (2014). Optimal analysis of best fit bin packing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 1 ed., Vol. 8572 LNCS, pp. 429-441). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8572 LNCS, No. PART 1). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_36

Optimal analysis of best fit bin packing. / Dósa, György; Sgall, Jiří.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8572 LNCS PART 1. ed. Springer Verlag, 2014. p. 429-441 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8572 LNCS, No. PART 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dósa, G & Sgall, J 2014, Optimal analysis of best fit bin packing. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 1 edn, vol. 8572 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 8572 LNCS, Springer Verlag, pp. 429-441, 41st International Colloquium on Automata, Languages, and Programming, ICALP 2014, Copenhagen, Denmark, 7/8/14. https://doi.org/10.1007/978-3-662-43948-7_36
Dósa G, Sgall J. Optimal analysis of best fit bin packing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 1 ed. Vol. 8572 LNCS. Springer Verlag. 2014. p. 429-441. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). https://doi.org/10.1007/978-3-662-43948-7_36
Dósa, György ; Sgall, Jiří. / Optimal analysis of best fit bin packing. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8572 LNCS PART 1. ed. Springer Verlag, 2014. pp. 429-441 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).
@inproceedings{15f0c44fc05b477c967e4b3426fd383c,
title = "Optimal analysis of best fit bin packing",
abstract = "In early seventies it was shown that the asymptotic approximation ratio of BestFit bin packing is equal to 1.7. We prove that also the absolute approximation ratio for BestFit bin packing is exactly 1.7, improving the previous bound of 1.75. This means that if the optimum needs Opt bins, BestFit always uses at most ⌊1.7·OPT⌋ bins. Furthermore we show matching lower bounds for all values of Opt, i.e., we give instances on which BestFit uses exactly ⌊1.7·OPT⌋ bins. Thus we completely settle the worst-case complexity of BestFit bin packing after more than 40 years of its study.",
author = "Gy{\"o}rgy D{\'o}sa and Jiř{\'i} Sgall",
year = "2014",
doi = "10.1007/978-3-662-43948-7_36",
language = "English",
isbn = "9783662439470",
volume = "8572 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
number = "PART 1",
pages = "429--441",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
edition = "PART 1",

}

TY - GEN

T1 - Optimal analysis of best fit bin packing

AU - Dósa, György

AU - Sgall, Jiří

PY - 2014

Y1 - 2014

N2 - In early seventies it was shown that the asymptotic approximation ratio of BestFit bin packing is equal to 1.7. We prove that also the absolute approximation ratio for BestFit bin packing is exactly 1.7, improving the previous bound of 1.75. This means that if the optimum needs Opt bins, BestFit always uses at most ⌊1.7·OPT⌋ bins. Furthermore we show matching lower bounds for all values of Opt, i.e., we give instances on which BestFit uses exactly ⌊1.7·OPT⌋ bins. Thus we completely settle the worst-case complexity of BestFit bin packing after more than 40 years of its study.

AB - In early seventies it was shown that the asymptotic approximation ratio of BestFit bin packing is equal to 1.7. We prove that also the absolute approximation ratio for BestFit bin packing is exactly 1.7, improving the previous bound of 1.75. This means that if the optimum needs Opt bins, BestFit always uses at most ⌊1.7·OPT⌋ bins. Furthermore we show matching lower bounds for all values of Opt, i.e., we give instances on which BestFit uses exactly ⌊1.7·OPT⌋ bins. Thus we completely settle the worst-case complexity of BestFit bin packing after more than 40 years of its study.

UR - http://www.scopus.com/inward/record.url?scp=84904161750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904161750&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-43948-7_36

DO - 10.1007/978-3-662-43948-7_36

M3 - Conference contribution

AN - SCOPUS:84904161750

SN - 9783662439470

VL - 8572 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 429

EP - 441

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -