Biased random walks, lyapunov functions, and stochastic analysis of best fit bin packing (Preliminary Version)

Claire Kenyon, Yuval Rabani, Alistair Sinclair

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 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 recently by Coffman et al [4]. It is also the first result which involves a detailed analysis of the infinite rnulti-dimensional Markov chain underlying the algorithm.

Original languageAmerican English
Title of host publicationProceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996
PublisherAssociation for Computing Machinery
Pages351-358
Number of pages8
ISBN (Electronic)0898713668
StatePublished - 28 Jan 1996
Externally publishedYes
Event7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 - Atlanta, United States
Duration: 28 Jan 199630 Jan 1996

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
VolumePart F129447

Conference

Conference7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996
Country/TerritoryUnited States
CityAtlanta
Period28/01/9630/01/96

Bibliographical note

Funding Information:
t CNRS, Ecole Normale Superieure de Lyon, France. E-mail: kenyonQlip.ens-lyon.fr. Work done while this author was visiting UC Berkeley, partially supported by a NATO Fellowship. SFaculty of Computer Science, Technion, Haifa 32000, Israel. E-mail: rabaniQcs . technion .ac. il. Work done while this author was a postdoctoral fellow in the Department of Computer Science, University of Toronto. §C!omputer Science Division, University of California, Berkeley CA 94720-1776. Email: sinclairQcs.berkeley.edu. Supported by NSF grant CCR-9505448 and a UC Berkeley Faculty Research Grant.

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