A compact encoding of plane triangulations with efficient query supports

Authors:
Katsuhisa Yamanaka;Shin-ichi Nakano
Affiliations:
Graduate School of Information Systems, University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo, 182-8585 Japan;Department of Computer Science, Gunma University, Tenjin-cho 1-5-1, Kiryu, Gunma, 376-8515 Japan
Venue:
Information Processing Letters
Year:
2010

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Abstract

In this paper we present a coding scheme for plane triangulations. The coding scheme is very simple, and needs only 6n bits for each plane triangulation with n vertices. Also with additional o(n) bits it supports adjacency, degree and clockwise neighbour queries in constant time. Our scheme is based on a realizer of a plane triangulation. The best known algorithm needs only 4.35n+o(n) bits for each plane triangulation. Our algorithm is simple and needs 6n+o(n) bits for each plane triangulation.