Self-adjusting binary search trees
Journal of the ACM (JACM)
Implicit data structures for weighted elements
Information and Control - The MIT Press scientific computation series
Planar point location using persistent search trees
Communications of the ACM
A new proof of the Garsia-Wachs algorithm
Journal of Algorithms
A fast planar partition algorithm, I
Journal of Symbolic Computation
Computational Geometry: Theory and Applications
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
Alternatives to splay trees with O(log n) worst-case access times
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Weighted Multidimensional B-trees Used as Nearly Optimal Dynamic Dictionaries
Proceedings on Mathematical Foundations of Computer Science
Efficient Expected-Case Algorithms for Planar Point Location
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Improved Upper Bounds for Pairing Heaps
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Three Major Extensions to Kirkpatrick's Point Location Algorithm
CGI '96 Proceedings of the 1996 Conference on Computer Graphics International
Nearly optimal expected-case planar point location
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Efficient dynamic programming using quadrangle inequalities
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Expected asymptotically optimal planar point location
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
A simple entropy-based algorithm for planar point location
ACM Transactions on Algorithms (TALG)
Optimal Expected-Case Planar Point Location
SIAM Journal on Computing
Distribution-sensitive point location in convex subdivisions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Dynamic optimality for skip lists and B-trees
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Applications of a planar separator theorem
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Entropy, triangulation, and point location in planar subdivisions
ACM Transactions on Algorithms (TALG)
Practical distribution-sensitive point location in triangulations
Computer Aided Geometric Design
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In the past ten years, there have been a number of data structures that, given a distribution of planar point location queries, produce a planar point location data structure that is tuned for the provided distribution. These structures all suffer from the requirement that the query distribution be provided in advance. For the problem of point location in a triangulation, a data structure is presented that performs asymptotically as well as these structures, but does not require the distribution to be provided in advance. This result is the 2-d analogue of the jump from the optimum binary search trees of Knuth in 1971 which required that the distribution be provided, to the splay trees of Sleator and Tarjan in 1985 where in the static optimality theorem it was proven that splay trees had the same asymptotic performance of optimum search trees without being provided the probability distribution.