Biased Random Walks, Lyapunov Functions, and Stochastic Analysis of Best Fit Bin Packing

Claire Kenyon*, Yuval Rabani, Alistair Sinclair

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We study the average case performance of the Best Fit algorithm for on-line bin packing under the distribution U{j, k}, in which the item sizes are uniformly distributed in the discrete range {1/k, 2/k, . . . , j/k}. Our main result is that, in the case j = k - 2, the expected waste for an infinite stream of items remains bounded. This settles an open problem posed by Coffman et al. [4]. It is also the first result which involves a detailed analysis of the infinite multidimensional Markov chain underlying the algorithm.

Original languageAmerican English
Pages (from-to)218-235
Number of pages18
JournalJournal of Algorithms
Volume27
Issue number2
DOIs
StatePublished - May 1998
Externally publishedYes

Bibliographical note

Funding Information:
³Supported by NSF Grant CCR-9505448 and a UC Berkeley Faculty Research Grant. E-mail: sinclair@cs.berkeley.edu.

Funding Information:
We study the average case performance of the Best Fit algorithm for on-line bin packing under the distribution U j, k4, in which the item sizes are uniformly distributed in the discrete range 1rk,2rk,..., jrk4. Our main result is that, in the case j s k y 2, the expected waste for an infinite stream of items remains bounded. This settles an open problem posed by Coffman et al. w4x. It is also the first result which involves a detailed analysis of the infinite multidimensional Markov chain underlying the algorithm. Q 1998 Academic Press * Work done while the author was visiting UC Berkeley, partially supported by a NATO Fellowship. E-mail: Claire.Kenyon@Lri.fr.

Funding Information:
² Most of this work was done while the author was a postdoctoral fellow in the Department of Computer Science, University of Toronto. Work at the Technion supported in part by a David and Ruth Moskowitz Academic Lectureship award and by a grant from the Technion fund for the promotion of sponsored research. E-mail: rabani@cs.technion.ac.il.

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