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
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
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
Computing Homotopic Shortest Paths Efficiently
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Computing homotopic shortest paths efficiently
Computational Geometry: Theory and Applications
Thick non-crossing paths and minimum-cost flows in polygonal domains
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Mutually visible agents in a discrete environment
ACSC '07 Proceedings of the thirtieth Australasian conference on Computer science - Volume 62
Computing homotopic shortest paths efficiently
Computational Geometry: Theory and Applications
A bug-inspired algorithm for efficient anytime path planning
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Fréchet distance of surfaces: some simple hard cases
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
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
Optimal paths for mutually visible agents
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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 address the problem of computing homotopic shortest paths in the presence of obstacles in the plane. Problems on homotopy of paths received attention very recently [Cabello et al., in: Proc. 18th Annu. ACM Sympos. Comput. Geom., 2002, pp. 160-169; Efrat et al., in: Proc. 10th Annu. European Sympos. Algorithms, 2002, pp. 411-423]. We present two output-sensitive algorithms, for simple paths and non-simple paths. The algorithm for simple paths improves the previous algorithm [Efrat et al., in: Proc. 10th Annu. European Sympos. Algorithms, 2002, pp. 411-423]. The algorithm for non-simple paths achieves O(log2n) time per output vertex which is an improvement by a factor of O(n/log2n) of the previous algorithm [Hershberger, Snoeyink, Comput. Geom. Theory Appl. 4 (1994) 63-98], where n is the number of obstacles. The running time has an overhead O(n2+ε) for any positive constant ε. In the case k 2+ε, where k is the total size of the input and output, we improve the running to O((n + k + (nk)2/3) logO(1) n).