Short encodings of planar graphs and maps
Discrete Applied Mathematics
Compact pat trees
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Linear-Time Succinct Encodings of Planar Graphs via Canonical Orderings
SIAM Journal on Discrete Mathematics
Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Succinct Representation of Balanced Parentheses and Static Trees
SIAM Journal on Computing
A Fast General Methodology for Information-Theoretically Optimal Encodings of Graphs
SIAM Journal on Computing
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Orderly Spanning Trees with Applications
SIAM Journal on Computing
Optimal succinct representations of planar maps
Proceedings of the twenty-second annual symposium on Computational geometry
Balanced parentheses strike back
ACM Transactions on Algorithms (TALG)
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Optimal coding and sampling of triangulations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Succinct representation of triangulations with a boundary
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
A compact encoding of plane triangulations with efficient query supports
Information Processing Letters
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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 (log n)/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.