Characterizing and recognizing the visibility graph of a funnel-shaped polygon |
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Authors: | Seung-Hak Choi Sung Yong Shin Kyung-Yong Chwa |
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Affiliation: | (1) Core Technology Research Center, Samsung Advanced Institute of Technology, P.O. Box 111, 440-600 Suwon, Korea;(2) Department of Computer Science, Korea Advanced Institute of Science and Technology, Kusong-dong 373-1 Yusong-gu, 305-701 Taejon, Korea |
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Abstract: | A funnel, which is notable for its fundamental role in visibility algorithms, is defined as a polygon that has exactly three convex vertices, two of which are connected by a boundary edge. In this paper we investigate the visibility graph of a funnel which we call an F-graph.We first present two characterizations of an F-graph, one of whose sufficiency proof itself is a linear time Real RAM algorithm for drawing a funnel on the plane that corresponds to an F-graph. We next give a linear-time algorithm for recognizing an F-graph. When the algorithm recognizes an F-graph, it also reports one of the Hamiltonian cycles defining the boundary of its corresponding funnel. This recognition algorithm takes linear time even on a RAM.We finally show that an F-graph is weakly triangulated and therefore perfect, which agrees with the fact that perfect graphs are related to geometric structures.This work was supported in part by the Korea Science and Engineering Foundation under Grant 91-01-01. |
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Keywords: | Computational geometry Funnel-shaped polygon Visibility graph Characterizing and recognizing visibility graphs Weakly triangulated graph Perfect graph |
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