TY - JOUR

T1 - Computing homotopic shortest paths efficiently

AU - Efrat, Alon

AU - Kobourov, Stephen G.

AU - Lubiw, Anna

N1 - Funding Information:
A preliminary version of this paper appeared in the 10th European Symposium on Algorithms (ESA), 2002, pp. 411–423. Corresponding author. E-mail addresses: alon@cs.arizona.edu (A. Efrat), kobourov@cs.arizona.edu (S.G. Kobourov), alubiw@uwaterloo.ca (A. Lubiw). 1 Partially supported by the NSF under grant ACR-0222920.

PY - 2006/10

Y1 - 2006/10

N2 - We give deterministic and randomized algorithms to find shortest paths homotopic to a given collection Π of disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k out+k inlogn+n√n), and the randomized algorithm runs in expected time O(k out+k inlogn+n(logn) 1+ε). Here k in is the number of edges in all the paths of Π, and k out is the number of edges in the output paths.

AB - We give deterministic and randomized algorithms to find shortest paths homotopic to a given collection Π of disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k out+k inlogn+n√n), and the randomized algorithm runs in expected time O(k out+k inlogn+n(logn) 1+ε). Here k in is the number of edges in all the paths of Π, and k out is the number of edges in the output paths.

KW - Homotopic shortest paths

KW - Shortest path in a polygon

UR - http://www.scopus.com/inward/record.url?scp=84867977487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867977487&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2006.03.003

DO - 10.1016/j.comgeo.2006.03.003

M3 - Article

AN - SCOPUS:84867977487

SN - 0925-7721

VL - 35

SP - 162

EP - 172

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 3

ER -