Affiliation:
1. University of Ljubljana, Slovenia and IMFM
2. Simon Fraser University
3. University of Illinois at Urbana-Champaign
Abstract
A cycle on a combinatorial surface is tight if it as short as possible in its (free) homotopy class. We describe an algorithm to compute a single tight, noncontractible, essentially simple cycle on a given orientable combinatorial surface in
O
(
n
log
n
) time. The only method previously known for this problem was to compute the globally shortest noncontractible or nonseparating cycle in
O
(min{
g
3
,
n
},
n
log
n
) time, where
g
is the genus of the surface. As a consequence, we can compute the shortest cycle freely homotopic to a chosen boundary cycle in
O
(
n
log
n
) time, a tight octagonal decomposition in
O
(
gn
log
n
) time, and a shortest contractible cycle enclosing a nonempty set of faces in
O
(
n
log
2
n
) time.
Funder
Javna Agencija za Raziskovalno Dejavnost RS
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
5 articles.
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