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
Computational geometry: algorithms and applications
Computational geometry: algorithms 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
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Walking your dog in the woods in polynomial time
Proceedings of the twenty-fourth annual symposium on Computational geometry
Testing contractibility in planar rips complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
Homotopic Fréchet distance between curves or, walking your dog in the woods in polynomial time
Computational Geometry: Theory and Applications
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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(kout + kin logn + n√n), and the randomized algorithm runs in expected time O(kout + kin logn + n(log n)1 + ε). Here kin is the number of edges in all the paths of Π, and kout is the number of edges in the output paths.