Computational geometry: an introduction
Computational geometry: an introduction
Hash functions for priority queues
Information and Control
Filtering search: a new approach to query answering
SIAM Journal on Computing
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Efficient data structures for range searching on a grid
Journal of Algorithms
Information and Computation
Lower bounds for orthogonal range searching: I. The reporting case
Journal of the ACM (JACM)
Lower bounds for orthogonal range searching: part II. The arithmetic model
Journal of the ACM (JACM)
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
Surpassing the information theoretic bound with fusion trees
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Lower bounds for off-line range searching
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Efficient 3-D range searching in external memory
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Algorithms for three-dimensional dominance searching in linear space
Information Processing Letters
On two-dimensional indexability and optimal range search indexing
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The P-range tree: a new data structure for range searching in secondary memory
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Fast linear expected-time alogorithms for computing maxima and convex hulls
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
A Lower Bound on the Complexity of Orthogonal Range Queries
Journal of the ACM (JACM)
Output-size sensitive algorithms for finding maximal vectors
SCG '85 Proceedings of the first annual symposium on Computational geometry
A new algorithm for rectangle enclosure reporting
Information Processing Letters
Multidimensional divide-and-conquer
Communications of the ACM
On a model of indexability and its bounds for range queries
Journal of the ACM (JACM)
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Time-space trade-offs for predecessor search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A data structure for multi-dimensional range reporting
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
An Optimal Worst Case Algorithm for Reporting Intersections of Rectangles
IEEE Transactions on Computers
A data structure for orthogonal range queries
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
More output-sensitive geometric algorithms
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
Space Efficient Multi-dimensional Range Reporting
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Transdichotomous Results in Computational Geometry, I: Point Location in Sublogarithmic Time
SIAM Journal on Computing
Instance-Optimal Geometric Algorithms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Orthogonal Range Reporting in Three and Higher Dimensions
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the twenty-sixth annual symposium on Computational geometry
Counting inversions, offline orthogonal range counting, and related problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Optimal succinctness for range minimum queries
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A fast algorithm for three-dimensional layers of maxima problem
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Top-k document retrieval in optimal time and linear space
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Path queries in weighted trees
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
A faster grammar-based self-index
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Two-Dimensional range diameter queries
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Higher-dimensional orthogonal range reporting and rectangle stabbing in the pointer machine model
Proceedings of the twenty-eighth annual symposium on Computational geometry
Fast relative lempel-ziv self-index for similar sequences
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Succinct indices for range queries with applications to orthogonal range maxima
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Fast local searches and updates in bounded universes
Computational Geometry: Theory and Applications
Worst-Case I/O-Efficient Skyline Algorithms
ACM Transactions on Database Systems (TODS)
Improved grammar-based compressed indexes
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On position restricted substring searching in succinct space
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Compressed indexes for text with wildcards
Theoretical Computer Science
Space-efficient data-analysis queries on grids
Theoretical Computer Science
Persistent Predecessor Search and Orthogonal Point Location on the Word RAM
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Sequential dependency computation via geometric data structures
Computational Geometry: Theory and Applications
Compact binary relation representations with rich functionality
Information and Computation
Extracting powers and periods in a word from its runs structure
Theoretical Computer Science
On reporting the L1 metric closest pair in a query rectangle
Information Processing Letters
Journal of Discrete Algorithms
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We present a number of new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model: We present two data structures for 2-d orthogonal range emptiness. The first achieves O(n lg lg n) space and O(lg lg n) query time, assuming that the n given points are in rank space. This improves the previous results by Alstrup, Brodal, and Rauhe (FOCS'00), with O(n lgε n) space and O(lg lg n) query time, or with O(n lg lg n) space and O(lg2lg n) query time. Our second data structure uses O(n) space and answers queries in O(lgε n) time. The best previous O(n)-space data structure, due to Nekrich (WADS'07), answers queries in O(lg n/lg lg n) time. We give a data structure for 3-d orthogonal range reporting with O(n lg1+ε n) space and O(lg lg n + k) query time for points in rank space, for any constant ε0. This improves the previous results by Afshani (ESA'08), Karpinski and Nekrich (COCOON'09), and Chan (SODA'11), with O(n lg3 n) space and O(lg lg n + k) query time, or with O(n lg1+εn) space and O(lg2lg n + k) query time. Consequently, we obtain improved upper bounds for orthogonal range reporting in all constant dimensions above 3. Our approach also leads to a new data structure for 2D orthogonal range minimum queries with O(n lgε n) space and O(lg lg n) query time for points in rank space. We give a randomized algorithm for 4-d offline dominance range reporting/emptiness with running time O(n log n) plus the output size. This resolves two open problems (both appeared in Preparata and Shamos' seminal book): given a set of n axis-aligned rectangles in the plane, we can report all k enclosure pairs (i.e., pairs (r1,r2) where rectangle r1 completely encloses rectangle r2) in O(n lg n + k) expected time; given a set of n points in 4-d, we can find all maximal points (points not dominated by any other points) in O(n lg n) expected time. The most recent previous development on (a) was reported back in SoCG'95 by Gupta, Janardan, Smid, and Dasgupta, whose main result was an O([n lg n + k] lg lg n) algorithm. The best previous result on (b) was an O(n lg n lg lg n) algorithm due to Gabow, Bentley, and Tarjan---from STOC'84! As a consequence, we also obtain the current-record time bound for the maxima problem in all constant dimensions above~4.