Efficient approximation algorithms for shortest cycles in undirected graphs
We describe a simple combinatorial approximation algorithm for finding a shortest (simple) cycle in an undirected graph. Given an adjacency-list representation of an undirected graph G with n vertices and unknown girth k, our algorithm returns with high probability a cycle of length at most 2 k for...
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| Vydáno v: | Information processing letters Ročník 109; číslo 10; s. 493 - 498 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
30.04.2009
Elsevier Elsevier Sequoia S.A |
| Témata: | |
| ISSN: | 0020-0190, 1872-6119 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We describe a simple combinatorial approximation algorithm for finding a shortest (simple) cycle in an undirected graph. Given an adjacency-list representation of an undirected graph
G with
n vertices and unknown girth
k, our algorithm returns with high probability a cycle of length at most 2
k for even
k and
2
k
+
2
for odd
k, in time
O
(
n
3
2
log
n
)
. Thus, in general, it yields a
2
2
3
approximation. For a weighted, undirected graph, with non-negative edge weights in the range
{
1
,
2
,
…
,
M
}
, we present a simple combinatorial 2-approximation algorithm for a minimum weight (simple) cycle that runs in time
O
(
n
2
log
n
(
log
n
+
log
M
)
)
. |
|---|---|
| Bibliografie: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| ISSN: | 0020-0190 1872-6119 |
| DOI: | 10.1016/j.ipl.2009.01.008 |