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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| Veröffentlicht in: | Algorithmica Jg. 79; H. 1; S. 211 - 229 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.09.2017
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 0178-4617, 1432-0541 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
|---|---|
| Bibliographie: | 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 |