Computational Geometry: Theory and Applications
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Methods for achieving fast query times in point location data structures
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Entropy-preserving cuttings and space-efficient planar point location
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A simple entropy-based algorithm for planar point location
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Nearly optimal expected-case planar point location
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A simple entropy-based algorithm for planar point location
ACM Transactions on Algorithms (TALG)
Lower bounds for expected-case planar point location
Computational Geometry: Theory and Applications
Distribution-sensitive point location in convex subdivisions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A static optimality transformation with applications to planar point location
Proceedings of the twenty-seventh annual symposium on Computational geometry
Succinct geometric indexes supporting point location queries
ACM Transactions on Algorithms (TALG)
Entropy, triangulation, and point location in planar subdivisions
ACM Transactions on Algorithms (TALG)
A self-adjusting data structure for multidimensional point sets
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Practical distribution-sensitive point location in triangulations
Computer Aided Geometric Design
Distance-Sensitive planar point location
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Given a fixed distribution of point location queries among the triangles in a triangulation of the plane, a data structure is presented that achieves, within constant multiplicative factors, the entropy bound on the expected point location query time. The data structure is a simple variation of Kirkpatrick's classic planar point location structure [D.G. Kirkpatrick, SIAM J. Comput. 12 (1) (1983) 28-35], and has linear construction costs and space requirements.