Optimal analysis of best fit bin packing

0440923 - MÚ 2015 DE eng C - Conference Paper (international conference)
Dósa, G. - Sgall, Jiří
Optimal analysis of best fit bin packing.
Automata, Languages, and Programming. Berlin: Springer, 2014 - (Esparza, J.; Fraigniaud, P.; Husfeldt, T.; Koutsoupias, E.), s. 429-441. Lecture Notes in Computer Science, 8572. ISBN 978-3-662-43947-0.
[41st International Colloquium, ICALP 2014. Copenhagen (DK), 08.07.2014-11.07.2014]
R&D Projects: GA ČR GBP202/12/G061
Keywords : approximation * packing
Subject RIV: BA - General Mathematics
http://link.springer.com/chapter/10.1007%2F978-3-662-43948-7_36

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.
Permanent Link: http://hdl.handle.net/11104/0243993