A new approximate graph coloring algorithm

Avi Wigderson

doi:10.1145/800070.802207

A new approximate graph coloring algorithm

Avi Wigderson^*

^*Corresponding author for this work

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

11 Scopus citations

Abstract

Let A be a graph coloring algorithm. Denote by Â(G) the ratio between the maximum number of colors A will use to color the graph C, and the chromatic number of G, χ(G). For most existing polynomial coloring algorithms, Â(G) can be as bad as O(n), where n is the number of vertices in G. The best currently known algorithm guarantees Â(G)-O(n/log n). In this paper we present a simple and efficient coloring algorithm which guarantees Â(G)≤_χ(G)n^1-1/χ(G)-1, a considerable improvement over the current bounds.

Original language	English
Title of host publication	Proceedings of the 14th Annual ACM Symposium on Theory of Computing, STOC 1982
Publisher	Association for Computing Machinery
Pages	325-329
Number of pages	5
ISBN (Print)	0897910702
DOIs	https://doi.org/10.1145/800070.802207
State	Published - 5 May 1982
Externally published	Yes
Event	14th Annual ACM Symposium on Theory of Computing, STOC 1982 - San Francisco, United States Duration: 5 May 1982 → 7 May 1982

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	14th Annual ACM Symposium on Theory of Computing, STOC 1982
Country/Territory	United States
City	San Francisco
Period	5/05/82 → 7/05/82

Bibliographical note

Publisher Copyright:
© 1982 ACM.

Access to Document

10.1145/800070.802207

Cite this

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title = "A new approximate graph coloring algorithm",

abstract = "Let A be a graph coloring algorithm. Denote by {\^A}(G) the ratio between the maximum number of colors A will use to color the graph C, and the chromatic number of G, χ(G). For most existing polynomial coloring algorithms, {\^A}(G) can be as bad as O(n), where n is the number of vertices in G. The best currently known algorithm guarantees {\^A}(G)-O(n/log n). In this paper we present a simple and efficient coloring algorithm which guarantees {\^A}(G)≤χ(G)n1-1/χ(G)-1, a considerable improvement over the current bounds.",

author = "Avi Wigderson",

note = "Publisher Copyright: {\textcopyright} 1982 ACM.; 14th Annual ACM Symposium on Theory of Computing, STOC 1982 ; Conference date: 05-05-1982 Through 07-05-1982",

year = "1982",

month = may,

day = "5",

doi = "10.1145/800070.802207",

language = "אנגלית",

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series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

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}

Wigderson, A 1982, A new approximate graph coloring algorithm. in Proceedings of the 14th Annual ACM Symposium on Theory of Computing, STOC 1982. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 325-329, 14th Annual ACM Symposium on Theory of Computing, STOC 1982, San Francisco, United States, 5/05/82. https://doi.org/10.1145/800070.802207

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N2 - Let A be a graph coloring algorithm. Denote by Â(G) the ratio between the maximum number of colors A will use to color the graph C, and the chromatic number of G, χ(G). For most existing polynomial coloring algorithms, Â(G) can be as bad as O(n), where n is the number of vertices in G. The best currently known algorithm guarantees Â(G)-O(n/log n). In this paper we present a simple and efficient coloring algorithm which guarantees Â(G)≤χ(G)n1-1/χ(G)-1, a considerable improvement over the current bounds.

AB - Let A be a graph coloring algorithm. Denote by Â(G) the ratio between the maximum number of colors A will use to color the graph C, and the chromatic number of G, χ(G). For most existing polynomial coloring algorithms, Â(G) can be as bad as O(n), where n is the number of vertices in G. The best currently known algorithm guarantees Â(G)-O(n/log n). In this paper we present a simple and efficient coloring algorithm which guarantees Â(G)≤χ(G)n1-1/χ(G)-1, a considerable improvement over the current bounds.

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ER -

A new approximate graph coloring algorithm

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