Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Representing dynamic binary trees succinctly
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Succinct indexable dictionaries with applications to encoding k-ary trees and multisets
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct Representation of Balanced Parentheses and Static Trees
SIAM Journal on Computing
Star-vertices: a compact representation for planar meshes with adjacency information
Journal of Graphics Tools
Compact representations of separable graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Static Dictionaries Supporting Rank
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
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
Computational Geometry: Theory and Applications
Optimal succinct representations of planar maps
Proceedings of the twenty-second annual symposium on Computational geometry
In-place 2-d nearest neighbor search
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Schnyder woods for higher genus triangulated surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Succinct representations of planar maps
Theoretical Computer Science
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Random accessible hierarchical mesh compression for interactive visualization
SGP '09 Proceedings of the Symposium on Geometry Processing
Succinct representation of labeled graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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
Succinct geometric indexes supporting point location queries
ACM Transactions on Algorithms (TALG)
Bounding the number of reduced trees, cographs, and series-parallel graphs by compression
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Explicit array-based compact data structures for triangulations
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We consider the problem of designing succinct geometric data structures while maintaining efficient navigation operations. A data structure is said succinct if the asymptotic amount of space it uses matches the entropy of the class of structures represented. For the case of planar triangulations with a boundary we propose a succinct representation of the combinatorial information that improves to 2.175 bits per triangle the asymptotic amount of space required and that supports the navigation between adjacent triangles in constant time (as well as other standard operations). For triangulations with m faces of a surface with genus g, our representation requires asymptotically an extra amount of 36(g - 1)lg m bits (which is negligible as long as g≪m/lg m).