Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Computational geometry: an introduction
Computational geometry: an introduction
Planar point location using persistent search trees
Communications of the ACM
An implicit data structure supporting insertion, deletion, and search in O(log:OS2:OEn) time
Journal of Computer and System Sciences
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of discrete and computational geometry
On the exact worst case query complexity of planar point location
Journal of Algorithms
Journal of Algorithms
Implicit dictionaries supporting searches and amortized updates in O(log n log log n) time
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Implicit B-Trees: New Results for the Dictionary Problem
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
An In-Place Sorting with O(n log n) Comparisons and O(n) Moves
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Space-efficient planar convex hull algorithms
Theoretical Computer Science - Latin American theorotical informatics
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Optimal succinct representations of planar maps
Proceedings of the twenty-second annual symposium on Computational geometry
Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time
Computational Geometry: Theory and Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Space-efficient geometric divide-and-conquer algorithms
Computational Geometry: Theory and Applications
Radix sorting with no extra space
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Succinct representation of triangulations with a boundary
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Line-segment intersection made in-place
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Optimal in-place algorithms for 3-D convex hulls and 2-D segment intersection
Proceedings of the twenty-fifth annual symposium on Computational geometry
Optimal in-place and cache-oblivious algorithms for 3-d convex hulls and 2-d segment intersection
Computational Geometry: Theory and Applications
Succinct geometric indexes supporting point location queries
ACM Transactions on Algorithms (TALG)
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We revisit a classic problem in computational geometry: preprocessing a planar n-point set to answer nearest neighbor queries. In SoCG 2004, Brönnimann, Chan, and Chen showed that it is possible to design an efficient data structure that takes no extra space at all other than the input array holding a permutation of the points. The best query time known for such "in-place data structures" is O(log2 n). In this paper, we break the O(log2 n) barrier by providing a method that answers nearest neighbor queries in time {display equation} The new method uses divide-and-conquer (based on planar separators) in a way that is quite unlike traditional point location methods, and extends previous 1-d data structuring techniques (specifically the van Emde Boas layout). The method has further applications, for example, in answering extreme point queries for a 3-d point set on the boundary of a convex set of constant complexity.