Algorithms for routing and testing routability of planar VLSI layouts
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
On continuous Homotopic one layer routing
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
Testing Homotopy for paths in the plane
Proceedings of the eighteenth annual symposium on Computational geometry
Proceedings of the eighteenth annual symposium on Computational geometry
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Computing homotopic shortest paths in the plane
Journal of Algorithms
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A theorem on polygon cutting with applications
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
River Routing Every Which Way, But Loose
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Algorithms and theory of computation handbook
Tightening Nonsimple Paths and Cycles on Surfaces
SIAM Journal on Computing
Homotopic rectilinear routing with few links and thick edges
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Shortest non-crossing walks in the plane
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Testing graph isotopies on surfaces
Proceedings of the twenty-eighth annual symposium on Computational geometry
GD'12 Proceedings of the 20th international conference on Graph Drawing
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We give deterministic and randomized algorithms to find shortest paths homotopic to a given collection @P of disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k"o"u"t+k"i"nlogn+nn), and the randomized algorithm runs in expected time O(k"o"u"t+k"i"nlogn+n(logn)^1^+^@e). Here k"i"n is the number of edges in all the paths of @P, and k"o"u"t is the number of edges in the output paths.