Dynamic Graph Coloring
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve different trade-offs between the number of recolorings and the numbe...
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| Vydané v: | Algorithmica Ročník 81; číslo 4; s. 1319 - 1341 |
|---|---|
| Hlavní autori: | , , , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.04.2019
Springer Nature B.V |
| Predmet: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve different trade-offs between the number of recolorings and the number of colors used. For any
d
>
0
, the first algorithm maintains a proper
O
(
C
d
N
1
/
d
)
-coloring while recoloring at most
O
(
d
) vertices per update, where
C
and
N
are the maximum chromatic number and maximum number of vertices, respectively. The second algorithm reverses the trade-off, maintaining an
O
(
C
d
)
-coloring with
O
(
d
N
1
/
d
)
recolorings per update. The two converge when
d
=
log
N
, maintaining an
O
(
C
log
N
)
-coloring with
O
(
log
N
)
recolorings per update. We also present a lower bound, showing that any algorithm that maintains a
c
-coloring of a 2-colorable graph on
N
vertices must recolor at least
Ω
(
N
2
c
(
c
-
1
)
)
vertices per update, for any constant
c
≥
2
. |
|---|---|
| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-018-0473-y |