On the performance guarantee of First Fit for sum coloring

Leah Epstein; Asaf Levin

doi:10.1016/j.jcss.2018.08.002

On the performance guarantee of First Fit for sum coloring

Leah Epstein, Asaf Levin

University of Haifa, Technion - Israel Institute of Technology

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

Abstract

In sum coloring, it is required to find a proper coloring of the vertices of a graph using positive integers, such that the sum of colors of the vertices is minimized. First Fit is the natural coloring algorithm that processes vertices one by one (in some order), and colors the current vertex with the minimum color that was not used for any of its already considered neighbors. Here, we study the approximation ratio of First Fit for sum coloring for the class of claw-free graphs, its most natural subclasses, and its generalizations, and get tight bounds for it.

Original language	American English
Pages (from-to)	91-105
Number of pages	15
Journal	Journal of Computer and System Sciences
Volume	99
DOIs	https://doi.org/10.1016/j.jcss.2018.08.002
State	Published - Feb 2019

Keywords

Approximation algorithm
Chromatic sum number of graphs
First Fit
Graph coloring

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.jcss.2018.08.002

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abstract = "In sum coloring, it is required to find a proper coloring of the vertices of a graph using positive integers, such that the sum of colors of the vertices is minimized. First Fit is the natural coloring algorithm that processes vertices one by one (in some order), and colors the current vertex with the minimum color that was not used for any of its already considered neighbors. Here, we study the approximation ratio of First Fit for sum coloring for the class of claw-free graphs, its most natural subclasses, and its generalizations, and get tight bounds for it.",

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AB - In sum coloring, it is required to find a proper coloring of the vertices of a graph using positive integers, such that the sum of colors of the vertices is minimized. First Fit is the natural coloring algorithm that processes vertices one by one (in some order), and colors the current vertex with the minimum color that was not used for any of its already considered neighbors. Here, we study the approximation ratio of First Fit for sum coloring for the class of claw-free graphs, its most natural subclasses, and its generalizations, and get tight bounds for it.

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KW - Chromatic sum number of graphs

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JF - Journal of Computer and System Sciences

ER -

On the performance guarantee of First Fit for sum coloring

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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