Tight results for Next Fit and Worst Fit with resource augmentation

Joan Boyar; Leah Epstein; Asaf Levin

doi:10.1016/j.tcs.2010.03.019

Tight results for Next Fit and Worst Fit with resource augmentation

Joan Boyar, Leah Epstein, Asaf Levin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is well known that the two simple algorithms for the classic bin packing problem, NF and WF both have an approximation ratio of 2. However, WF seems to be a more reasonable algorithm, since it never opens a new bin if an existing bin can still be used. Using resource augmented analysis, where the output of an approximation algorithm, which can use bins of size b > 1, is compared to an optimal packing into bins of size 1, we give a complete analysis of the asymptotic approximation ratio of WF and of NF, and use it to show that WF is strictly better than NF for any 1 < b < 2, while they have the same asymptotic performance guarantee for all b ≥ 2, and for b = 1.

Original language	English
Pages (from-to)	2572-2580
Number of pages	9
Journal	Theoretical Computer Science
Volume	411
Issue number	26-28
DOIs	https://doi.org/10.1016/j.tcs.2010.03.019
State	Published - 6 Jun 2010

Bibliographical note

Funding Information:
The authors gratefully acknowledge support from the National Natural Science Foundation of China (91434202, 21506127), the Program for Changjiang Scholars and Innovative Research Team in University (IRT15R48), State Key Laboratory of Polymer Materials Engineering (sklpme2014-1-01), and State Key Laboratory of Separation Membranes and Membrane Processes (Tianjin Polytechnic University, No. M2-201506).

Keywords

Bin packing
Next Fit
Resource augmentation
Worst Fit

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.tcs.2010.03.019

Cite this

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title = "Tight results for Next Fit and Worst Fit with resource augmentation",

abstract = "It is well known that the two simple algorithms for the classic bin packing problem, NF and WF both have an approximation ratio of 2. However, WF seems to be a more reasonable algorithm, since it never opens a new bin if an existing bin can still be used. Using resource augmented analysis, where the output of an approximation algorithm, which can use bins of size b > 1, is compared to an optimal packing into bins of size 1, we give a complete analysis of the asymptotic approximation ratio of WF and of NF, and use it to show that WF is strictly better than NF for any 1 < b < 2, while they have the same asymptotic performance guarantee for all b ≥ 2, and for b = 1.",

keywords = "Bin packing, Next Fit, Resource augmentation, Worst Fit",

author = "Joan Boyar and Leah Epstein and Asaf Levin",

note = "Funding Information: The authors gratefully acknowledge support from the National Natural Science Foundation of China (91434202, 21506127), the Program for Changjiang Scholars and Innovative Research Team in University (IRT15R48), State Key Laboratory of Polymer Materials Engineering (sklpme2014-1-01), and State Key Laboratory of Separation Membranes and Membrane Processes (Tianjin Polytechnic University, No. M2-201506).",

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AU - Epstein, Leah

AU - Levin, Asaf

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N2 - It is well known that the two simple algorithms for the classic bin packing problem, NF and WF both have an approximation ratio of 2. However, WF seems to be a more reasonable algorithm, since it never opens a new bin if an existing bin can still be used. Using resource augmented analysis, where the output of an approximation algorithm, which can use bins of size b > 1, is compared to an optimal packing into bins of size 1, we give a complete analysis of the asymptotic approximation ratio of WF and of NF, and use it to show that WF is strictly better than NF for any 1 < b < 2, while they have the same asymptotic performance guarantee for all b ≥ 2, and for b = 1.

AB - It is well known that the two simple algorithms for the classic bin packing problem, NF and WF both have an approximation ratio of 2. However, WF seems to be a more reasonable algorithm, since it never opens a new bin if an existing bin can still be used. Using resource augmented analysis, where the output of an approximation algorithm, which can use bins of size b > 1, is compared to an optimal packing into bins of size 1, we give a complete analysis of the asymptotic approximation ratio of WF and of NF, and use it to show that WF is strictly better than NF for any 1 < b < 2, while they have the same asymptotic performance guarantee for all b ≥ 2, and for b = 1.

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KW - Resource augmentation

KW - Worst Fit

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Tight results for Next Fit and Worst Fit with resource augmentation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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