Optimal Pants Decompositions and Shortest Homotopic Cycles on an Orientable SurfaceDe Verdière, Éric Colin and Lazarus, Francis (2004) Optimal Pants Decompositions and Shortest Homotopic Cycles on an Orientable Surface. In: Graph Drawing 11th International Symposium, GD 2003, September 2124, 2003 , pp. 478490(Official URL: http://dx.doi.org/10.1007/9783540245957_45). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783540245957_45
AbstractA pants decomposition of a compact orientable surface M is a set of disjoint simple cycles which cuts M into pairs of pants, i.e., spheres with three boundaries. Assuming M is a polyhedral surface, with weighted vertexedge graph G, we consider combinatorial pants decompositions: the cycles are closed walks in G that may overlap but do not cross. We give an algorithm which, given a pants decomposition, computes a homotopic pants decomposition in which each cycle is a shortest cycle in its homotopy class. In particular, the resulting decomposition is optimal (as short as possible among all homotopic pants decompositions), and any optimal pants decomposition is made of shortest homotopic cycles. Our algorithm is polynomial in the complexity of the input and in the longesttoshortest edge ratio of G. The same algorithm can be applied, given a simple cycle C, to compute a shortest cycle homotopic to C which is itself simple.
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