Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Compact representations of separable graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Fast General Methodology for Information - Theoretically Optimal Encodings of Graphs
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Dissections and trees, with applications to optimal mesh encoding and to random sampling
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling
ACM Transactions on Algorithms (TALG)
Balanced parentheses strike back
ACM Transactions on Algorithms (TALG)
Schnyder woods for higher genus triangulated surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Visibility representations of four-connected plane graphs with near optimal heights
Computational Geometry: Theory and Applications
Optimal coding and sampling of triangulations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A fast and compact web graph representation
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
A compact encoding of plane triangulations with efficient query supports
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
A compact encoding of plane triangulations with efficient query supports
Information Processing Letters
GD'09 Proceedings of the 17th international conference on Graph Drawing
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Let G be an embedded planar undirected graph that has n vertices, m edges, and f faces but has no self-loop or multiple edge. If G is triangulated, we can encode it using 4/3m-1 bits, improving on the best previous bound of about 1.53m bits. In case exponential time is acceptable, roughly 1.08m bits have been known to suffice. If G is triconnected, we use at most $(2.5+2\log{3})\min\{n,f\}-7$ bits, which is at most 2.835m bits and smaller than the best previous bound of 3m bits. Both of our schemes take O(n) time for encoding and decoding.