Abstract
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).
This work has been supported by the French “ACI Masses de données” program, via the Geocomp project, http://www.lix.polytechnique.fr/ schaeffe/GeoComp/.
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References
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Aleardi, L.C., Devillers, O., Schaeffer, G. (2005). Succinct Representation of Triangulations with a Boundary. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_13
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DOI: https://doi.org/10.1007/11534273_13
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