Best fit bin packing with random order revisited

Albers, S and Khan, A and Ladewig, L (2020) Best fit bin packing with random order revisited. In: 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020, 25-26 August 2020, Prague; Czech Republic.

PDF lei_int_pro_inf_lip_170_2020.pdf - Published Version Restricted to Registered users only Download (641kB) | Request a copy

Abstract

Best Fit is a well known online algorithm for the bin packing problem, where a collection of one-dimensional items has to be packed into a minimum number of unit-sized bins. In a seminal work, Kenyon SODA 1996 introduced the (asymptotic) random order ratio as an alternative performance measure for online algorithms. Here, an adversary specifies the items, but the order of arrival is drawn uniformly at random. Kenyon's result establishes lower and upper bounds of 1.08 and 1.5, respectively, for the random order ratio of Best Fit. Although this type of analysis model became increasingly popular in the field of online algorithms, no progress has been made for the Best Fit algorithm after the result of Kenyon. We study the random order ratio of Best Fit and tighten the long-standing gap by establishing an improved lower bound of 1.10. For the case where all items are larger than 1/3, we show that the random order ratio converges quickly to 1.25. It is the existence of such large items that crucially determines the performance of Best Fit in the general case. Moreover, this case is closely related to the classical maximum-cardinality matching problem in the fully online model. As a side product, we show that Best Fit satisfies a monotonicity property on such instances, unlike in the general case. In addition, we initiate the study of the absolute random order ratio for this problem. In contrast to asymptotic ratios, absolute ratios must hold even for instances that can be packed into a small number of bins. We show that the absolute random order ratio of Best Fit is at least 1.3. For the case where all items are larger than 1/3, we derive upper and lower bounds of 21/16 and 1.2, respectively. © Nathalie Bertrand; licensed under Creative Commons License CC-BY 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020).

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright of this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Keywords:	Bin packing problem; Cardinality matching; Lower and upper bounds; Monotonicity property; On-line algorithms; Performance measure; Random order ratio; Upper and lower bounds, One dimensional
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	27 Oct 2020 06:54
Last Modified:	27 Oct 2020 06:54
URI:	http://eprints.iisc.ac.in/id/eprint/66603

Actions (login required)

View Item