Abstract
In this paper we give 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, however, within o(n) bits it needs to store a complete list of all possible triangulations having at most (logn)/4 nodes, while our algorithm is simple and does not need such a list. The second best known algorithm needs 2m + (5 + 1/k)n + o(m + n) bits for each (general) plane graph with m edges and 7n + o(n) bits for each plane triangulation, while our algorithm needs only 6n + o(n) bits for each plane triangulation.
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Yamanaka, K., Nakano, Si. (2008). A Compact Encoding of Plane Triangulations with Efficient Query Supports. In: Nakano, Si., Rahman, M.S. (eds) WALCOM: Algorithms and Computation. WALCOM 2008. Lecture Notes in Computer Science, vol 4921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77891-2_12
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DOI: https://doi.org/10.1007/978-3-540-77891-2_12
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