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Computing contour trees in all dimensions
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Computing homotopic shortest paths in the plane
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Loops in Reeb Graphs of 2-Manifolds
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Greedy optimal homotopy and homology generators
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Tightening non-simple paths and cycles on surfaces
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Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
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Computing homotopic shortest paths efficiently
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Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Surface matching using consistent pants decomposition
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Finding shortest contractible and shortest separating cycles in embedded graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Minimum cuts and shortest homologous cycles
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Finding shortest contractible and shortest separating cycles in embedded graphs
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Shortest cut graph of a surface with prescribed vertex set
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Technical Section: Tiling surfaces with cylinders using n-loops
Computers and Graphics
Tightening Nonsimple Paths and Cycles on Surfaces
SIAM Journal on Computing
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Shortest non-crossing walks in the plane
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Minimum cuts and shortest non-separating cycles via homology covers
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
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We consider the problem of finding a shortest cycle (freely) homotopic to a given simple cycle on a compact, orientable surface. For this purpose, we use a pants decomposition of the surface: a set of disjoint simple cycles that cut the surface into pairs of pants (spheres with three holes). We solve this problem in a framework where the cycles are closed walks on the vertex-edge graph of a combinatorial surface that may overlap but do not cross. We give an algorithm that transforms an input pants decomposition into another homotopic pants decomposition that is optimal: each cycle is as short as possible in its homotopy class. As a consequence, finding a shortest cycle homotopic to a given simple cycle amounts to extending the cycle into a pants decomposition and to optimizing it: the resulting pants decomposition contains the desired cycle. We describe two algorithms for extending a cycle to a pants decomposition. All algorithms in this article are polynomial, assuming uniformity of the weights of the vertex-edge graph of the surface.