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

Claire Kenyon; Yuval Rabani; Alistair Sinclair

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 proceeding › Conference contribution › peer-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 language	English
Title of host publication	Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996
Publisher	Association for Computing Machinery
Pages	351-358
Number of pages	8
ISBN (Electronic)	0898713668
State	Published - 28 Jan 1996
Externally published	Yes
Event	7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 - Atlanta, United States Duration: 28 Jan 1996 → 30 Jan 1996

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume	Part F129447

Conference

Conference	7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996
Country/Territory	United States
City	Atlanta
Period	28/01/96 → 30/01/96

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.

Cite this

Kenyon, C., Rabani, Y., & Sinclair, A. (1996). Biased random walks, lyapunov functions, and stochastic analysis of best fit bin packing (Preliminary Version). In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 (pp. 351-358). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. Part F129447). Association for Computing Machinery.

Kenyon, Claire ; Rabani, Yuval ; Sinclair, Alistair. / Biased random walks, lyapunov functions, and stochastic analysis of best fit bin packing (Preliminary Version). Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996. Association for Computing Machinery, 1996. pp. 351-358 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

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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.",

author = "Claire Kenyon and Yuval Rabani and Alistair Sinclair",

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.; 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 ; Conference date: 28-01-1996 Through 30-01-1996",

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Kenyon, C, Rabani, Y & Sinclair, A 1996, Biased random walks, lyapunov functions, and stochastic analysis of best fit bin packing (Preliminary Version). in Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. Part F129447, Association for Computing Machinery, pp. 351-358, 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996, Atlanta, United States, 28/01/96.

Biased random walks, lyapunov functions, and stochastic analysis of best fit bin packing (Preliminary Version). / Kenyon, Claire; Rabani, Yuval; Sinclair, Alistair.
Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996. Association for Computing Machinery, 1996. p. 351-358 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. Part F129447).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

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Bibliographical note

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