Computational complexity of combinatorial surfaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Short encodings of planar graphs and maps
Discrete Applied Mathematics
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
On topological aspects of orientations
Discrete Mathematics
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Optimal System of Loops on an Orientable Surface
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
Efficient Edgebreaker for Surfaces of Arbitrary Topology
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
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
Optimal succinct representations of planar maps
Proceedings of the twenty-second annual symposium on Computational geometry
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Optimal Coding and Sampling of Triangulations
Algorithmica
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Succinct representation of labeled graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Succinct representation of triangulations with a boundary
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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Schnyder woods are a well known combinatorial structure for planar graphs, which yields a decomposition into 3 vertex-spanning trees. Our goal is to extend definitions and algorithms for Schnyder woods designed for planar graphs (corresponding to combinatorial surfaces with the topology of the sphere, i.e., of genus 0) to the more general case of graphs embedded on surfaces of arbitrary genus. First, we define a new traversal order of the vertices of a triangulated surface of genus g together with an orientation and coloration of the edges that extends the one proposed by Schnyder for the planar case. As a by-product we show how some recent schemes for compression and compact encoding of graphs can be extended to higher genus. All the algorithms presented here have linear time complexity.