On the absolute approximation ratio for First Fit and related results

Joan Boyar; György Dósa; Leah Epstein

doi:10.1016/j.dam.2012.04.012

On the absolute approximation ratio for First Fit and related results

Joan Boyar, György Dósa, Leah Epstein

Department of Mathematics

University of Haifa

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

Abstract

We revisit three famous bin packing algorithms, namely Next Fit (NF), Worst Fit (WF) and First Fit (FF). We compare the approximation ratio of these algorithms as a function of the total size of the input items α. We give a complete analysis of the worst case behavior of WF and NF, and determine the ranges of α for which FF has a smaller approximation ratio than WF and NF. In addition, we prove a new upper bound of 127≈1.7143 on the absolute approximation ratio of FF, improving over the previously known upper bound of 1.75, given by Simchi-Levi. This property of FF is in contrast to the absolute approximation ratios of WF and NF, which are both equal to 2.

Original language	American English
Pages (from-to)	1914-1923
Number of pages	10
Journal	Discrete Applied Mathematics
Volume	160
Issue number	13-14
DOIs	https://doi.org/10.1016/j.dam.2012.04.012
State	Published - Sep 2012

Keywords

Bin packing
First Fit
Next Fit
Worst Fit

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1016/j.dam.2012.04.012

Cite this

@article{2f783125d0634a67864310d8eb28017d,

title = "On the absolute approximation ratio for First Fit and related results",

abstract = "We revisit three famous bin packing algorithms, namely Next Fit (NF), Worst Fit (WF) and First Fit (FF). We compare the approximation ratio of these algorithms as a function of the total size of the input items α. We give a complete analysis of the worst case behavior of WF and NF, and determine the ranges of α for which FF has a smaller approximation ratio than WF and NF. In addition, we prove a new upper bound of 127≈1.7143 on the absolute approximation ratio of FF, improving over the previously known upper bound of 1.75, given by Simchi-Levi. This property of FF is in contrast to the absolute approximation ratios of WF and NF, which are both equal to 2.",

keywords = "Bin packing, First Fit, Next Fit, Worst Fit",

author = "Joan Boyar and Gy{\"o}rgy D{\'o}sa and Leah Epstein",

note = "Funding Information: The first author was partially supported by the Danish Council for Independent Research, Natural Sciences . The second author was partially supported by Project K-TET_10-1-2011-0064833, Algorithms and Visualization for difficult combinatorial optimization problems .",

year = "2012",

month = sep,

doi = "10.1016/j.dam.2012.04.012",

language = "American English",

volume = "160",

pages = "1914--1923",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

number = "13-14",

}

TY - JOUR

T1 - On the absolute approximation ratio for First Fit and related results

AU - Boyar, Joan

AU - Dósa, György

AU - Epstein, Leah

N1 - Funding Information: The first author was partially supported by the Danish Council for Independent Research, Natural Sciences . The second author was partially supported by Project K-TET_10-1-2011-0064833, Algorithms and Visualization for difficult combinatorial optimization problems .

PY - 2012/9

Y1 - 2012/9

N2 - We revisit three famous bin packing algorithms, namely Next Fit (NF), Worst Fit (WF) and First Fit (FF). We compare the approximation ratio of these algorithms as a function of the total size of the input items α. We give a complete analysis of the worst case behavior of WF and NF, and determine the ranges of α for which FF has a smaller approximation ratio than WF and NF. In addition, we prove a new upper bound of 127≈1.7143 on the absolute approximation ratio of FF, improving over the previously known upper bound of 1.75, given by Simchi-Levi. This property of FF is in contrast to the absolute approximation ratios of WF and NF, which are both equal to 2.

AB - We revisit three famous bin packing algorithms, namely Next Fit (NF), Worst Fit (WF) and First Fit (FF). We compare the approximation ratio of these algorithms as a function of the total size of the input items α. We give a complete analysis of the worst case behavior of WF and NF, and determine the ranges of α for which FF has a smaller approximation ratio than WF and NF. In addition, we prove a new upper bound of 127≈1.7143 on the absolute approximation ratio of FF, improving over the previously known upper bound of 1.75, given by Simchi-Levi. This property of FF is in contrast to the absolute approximation ratios of WF and NF, which are both equal to 2.

KW - Bin packing

KW - First Fit

KW - Next Fit

KW - Worst Fit

UR - http://www.scopus.com/inward/record.url?scp=84862207658&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2012.04.012

DO - 10.1016/j.dam.2012.04.012

M3 - Article

SN - 0166-218X

VL - 160

SP - 1914

EP - 1923

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 13-14

ER -

On the absolute approximation ratio for First Fit and related results

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this