Parameterized and Approximation Algorithms for the Load Coloring Problem

Let c , k be two positive integers. Given a graph G = ( V , E ) , the c - Load Coloring problem asks whether there is a c -coloring φ : V → [ c ] such that for every i ∈ [ c ] , there are at least k edges with both endvertices colored i . Gutin and Jones (Inf Process Lett 114:446–449, 2014 ) studie...

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Vydáno v:	Algorithmica Ročník 79; číslo 1; s. 211 - 229
Hlavní autoři:	Barbero, F., Gutin, G., Jones, M., Sheng, B.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.09.2017 Springer Nature B.V
Témata:	Algorithm Analysis and Problem Complexity Algorithms Approximation Coloring Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Decision trees Graph theory Integers Mathematical analysis Mathematics of Computing Theory of Computation Kernels Approximation algorithms Parameterized algorithms FPT Load coloring
ISSN:	0178-4617, 1432-0541
On-line přístup:	Získat plný text
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Popis
Shrnutí:	Let c , k be two positive integers. Given a graph G = ( V , E ) , the c - Load Coloring problem asks whether there is a c -coloring φ : V → [ c ] such that for every i ∈ [ c ] , there are at least k edges with both endvertices colored i . Gutin and Jones (Inf Process Lett 114:446–449, 2014 ) studied this problem with c = 2 . They showed 2- Load Coloring to be fixed-parameter tractable (FPT) with parameter k by obtaining a kernel with at most 7 k vertices. In this paper, we extend the study to any fixed c by giving both a linear-vertex and a linear-edge kernel. In the particular case of c = 2 , we obtain a kernel with less than 4 k vertices and less than 6 k + ( 3 + 2 ) k + 4 edges. These results imply that for any fixed c ≥ 2 , c - Load Coloring is FPT and the optimization version of c - Load Coloring (where k is to be maximized) has an approximation algorithm with a constant ratio.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0178-4617 1432-0541
DOI:	10.1007/s00453-016-0259-z