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• W2100076445 abstract "Every compact orientable boundaryless surface /spl Mscr/ can be cut along simple loops with a common point /spl upsi//sub 0/, pairwise disjoint except at /spl upsi//sub 0/, so that the resulting surface is a topological disk; such a set of loops is called a fundamental system of loops for /spl Mscr/. The resulting disk is a polygon in which the edges are pairwise identified on the surface; it is called a polygonal schema Assuming that /spl Mscr/ is triangulated, and that each edge has a given length, we are interested in a shortest (or optimal) system homotopic to a given one, drawn on the vertex-edge graph of /spl Mscr/. We prove that each loop of such an optimal system is a shortest loop among all simple loops in its homotopy class. We give a polynomial (under some reasonable assumptions) algorithm to build such a system. As a byproduct, we get a polynomial algorithm to compute a shortest simple loop homotopic to a given simple loop." @default.
• W2100076445 created "2016-06-24" @default.
• W2100076445 creator A5044057604 @default.
• W2100076445 creator A5059014964 @default.
• W2100076445 date "2003-06-26" @default.
• W2100076445 modified "2023-10-13" @default.
• W2100076445 title "Optimal system of loops on an orientable surface" @default.
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• W2100076445 doi "https://doi.org/10.1109/sfcs.2002.1181986" @default.
• W2100076445 hasPublicationYear "2003" @default.
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