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...
Uloženo v:
| Vydáno v: | Algorithmica Ročník 81; číslo 4; s. 1319 - 1341 |
|---|---|
| Hlavní autoři: | , , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.04.2019
Springer Nature B.V |
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| 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
. |
|---|---|
| Bibliografie: | 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 |