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.
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Communicated by Takao Nishizeki.
This work was supported in part by the Korea Science and Engineering Foundation under Grant 91-01-01.
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Choi, SH., Shin, S.Y. & Chwa, KY. Characterizing and recognizing the visibility graph of a funnel-shaped polygon. Algorithmica 14, 27–51 (1995). https://doi.org/10.1007/BF01300372
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DOI: https://doi.org/10.1007/BF01300372