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An optimal algorithm for closest pair maintenance (extended abstract)

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Sergei N. BespamyatnikhAuthors Info & Claims

SCG '95: Proceedings of the eleventh annual symposium on Computational geometry

Pages 152 - 161

https://doi.org/10.1145/220279.220296

Published: 01 September 1995 Publication History

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References

[1]

S. Arya and D. M. Mount. Approximate Nearest-Neighbor Queries in Fixed Dimensions. Proceedings 4th Annual Symposium on Discrete Algorithms, 1993, pp. 271-280.

Digital Library

Google Scholar

[2]

S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Wu. An Optimal Algorithm for Approximate Nearest- Neighbor Searching. Proceedings 5th Annual Symposium on Discrete Algorithms, 1994, pp. 573-582.

Digital Library

Google Scholar

[3]

S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Wu. An Optireal Algorithm for Approximate Nearest- Neighbor Searching. (revised version), 1994.

Google Scholar

[4]

M. Ben-Or. Lower Bounds for Algebraic Computation Trees. Proc. 15th Annual ACM Syrup. Theory Comput., 1983, pp. 80-86.

Digital Library

Google Scholar

[5]

S. W. Bent, D. D. Sleator and R.E. Tarjan Biased Search Trees. SIAM Journal of Computing, 1985, 14, pp. 545-568

Digital Library

Google Scholar

[6]

J. L. Bentley and M. I. Shamos. Divideand-Conquer in Multidimensional Space. Proc. 8th Annual ACM Syrup. Theory of Computing, 1976, pp. 220-230.

Digital Library

Google Scholar

[7]

M. Bern, D. Eppstein, and S.-H. Teng. Parallel Construction of Quadtrees and Quality Triangulations. Algorithms and Data Structures, Third Workshop, WADS '93, Lecture Notes in Computer Science 709, Springer-Verlag, 1993, pp. 188-199.

Digital Library

Google Scholar

[8]

S. N. Bespamyatnikh. The Region Approach for Some Dynamic Closest-Point Problems. Proc. 6th Canadian Conf. Comput. Geom., 1994.

Google Scholar

[9]

P. B. Callahan and S. R. Kosaraju. A Decomposition of Multi-Dimensional Point-Sets with Applications to k-Nearest-Neighbors and n- Body Potential Fields. Proceedings 24th Annual AMC Symposium on the Theory of Computing, 1992, pp. 546-556.

Digital Library

Google Scholar

[10]

P. B. Callahan and S. R. Kosaraju. Algorithms for Dynamic Closest Pair and n- Body Potential Fields. Proc. 6th Annual ACM-SIAM Symposium on Discrete Algorithms, 1995.

Digital Library

Google Scholar

[11]

Y.-J, Chiang, F. T. Prepe~rata, and R. Tamassia. A Unified Approach to Dynamic Point Location, Ray Shooting, and Shortest Paths in Planar Maps. Proc. 4th ACM-SIAM Symp. on Discrete Algorithms, 1993, pp. 44-53.

Digital Library

Google Scholar

[12]

R. F. Cohen and R. Tamassia. Combine and Conquer: a General Technique for Dynamic Algorithms. Proc. First Europ. Symp. on Algorithms, Lecture Notes in Computer Science. Springer-Verlag, 1993.

Digital Library

Google Scholar

[13]

M. J. Golin, R. Raman, C. Schwarz, and M. Smid. Randomized Data Structures for the Dynamic Closest-Pair Problem. Proc. 4th Annual ACM-SIAM Syrup. on Discrete Algorithms, 1993, pp. 301-310.

Digital Library

Google Scholar

[14]

M. J. Golin, R. Raman, C. Schwarz, and M. Smid. Simple Randomized Algorithms for Closest Pair Problems. Proc. 5th Canadian Conf. Comput. Geom., 1993, pp. 246-251.

Google Scholar

[15]

S. Kapoor and M. Smid. New Techniques for Exact and Approximate Dynamic Closest-Point Problems. Proc. 10th Annual ACM Symp. Comput. Geom., 1994, pp. 165-174.

Digital Library

Google Scholar

[16]

H.-P. Lenhof and M. Staid. Enumerating the k Closest Pair Optimally. Proc. 33rd Ann. IEEE Symp. Found. Comput. Sci., 1992, pp. 380-386.

Digital Library

Google Scholar

[17]

F. P. Preparata and M. I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, New York Berlin Heidelberg Tokyo, 1985.

Digital Library

Google Scholar

[18]

F. P. Preparata and M. I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, New York Berlin Heidelberg Tokyo, second edition, 1988.

Digital Library

Google Scholar

[19]

J. S. Salowe. Shallow Interdistance Selection and Interdistance Enumeration. International Journal of Computational Geometry & Applications, 2, 1992, pp. 49-59.

Google Scholar

[20]

M.I. Shamos and D. Hoey. Closest-Point Problem. Proc. 16th Annual IEEE Symp. Found. Comput. Sci., 1975, pp. 151-162.

Google Scholar

[21]

C. Schwarz. Data Structures and Algorithms for the Dynamic Closest Pair Problem. Ph.D. Thesis, Universit~t des Saarbrficken, 1993.

Google Scholar

[22]

C. Schwarz and M. Staid. An O(n log n log log n) Algorithm for the On-Line Closest Pair Problem. Proc. 3th ACM-SIAM Syrup. Discrete Algorithms, 1992, pp. 280-285.

Digital Library

Google Scholar

[23]

C. Schwarz, M. Staid, and J. Snoeyink. An Optimal Algorithm for the On-Line Closest-Pair Problem. Proc. 8th Annual ACM Syrup. Comput. Geom., 1992, pp. 330-336.

Digital Library

Google Scholar

[24]

D. D. Sleator and R. E. Tarjan. A Data Structure for Dynamic Trees. Journal of Computer and System Sciences, 26, 1983.

Digital Library

Google Scholar

[25]

M. Staid. Dynamic Rectangular Point Location, with an Application to the Closest Pair Problem. Technical Report MPI-I-91-101, Max-Plank-Institut ffirlnformatik, Saarbrficken, Germany, 1991

Google Scholar

[26]

M. Smid. Maintaining the Minimal Distance of a Point Set in Less Than Linear Time. Algorithms Rev., 2, 1991, pp. 33- 44.

Google Scholar

[27]

M. Staid. Maintaining the Minimal Distance of a Point Set in Polylogarithmic Time. Discrete & Computational Geometry, 7, 1992, pp. 415-431.

Digital Library

Google Scholar

[28]

K. L. Supowit. New Techniques for Some Dynamic Closest-Point and Farthest- Point Problems. Proc. 1-st Annual ACM-SiAM Symposium on Discrete Algorithms, 1990, pp. 84-90.

Digital Library

Google Scholar

[29]

P. M. Vaidya. An Optimal Algorithm for All-Nearest-Neighbors Problem. Proceedings 27th Annual Symposium Found. Comp. Sc., 1986, pp. 117- 122.

Digital Library

Google Scholar

[30]

P. M. Vaidya. An O(nlogn) Algorithm for All-Nearest-Neighbors Problem. Discrete Comput. Geom., 1989, pp. 101-115

Digital Library

Google Scholar

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An optimal algorithm for closest pair maintenance (extended abstract)

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SCG '95: Proceedings of the eleventh annual symposium on Computational geometry

September 1995

456 pages

ISBN:0897917243

DOI:10.1145/220279

Chairman:
Jack Snoeyink
Univ. of British Columbia, Vancouver, Canada

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Published: 01 September 1995

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June 5 - 7, 1995

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SCG '95 Paper Acceptance Rate 59 of 129 submissions, 46%;

Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Kurkure YShamo MWiseman JGalhotra SSintos S(2024)Faster Algorithms for Fair Max-Min Diversification in RdProceedings of the ACM on Management of Data10.1145/36549402:3(1-26)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654940
Jiang MQi XTejada P(2011)A Computational-Geometry Approach to Digital Image Contour ExtractionTransactions on Computational Science XIII10.1007/978-3-642-22619-9_2(13-43)Online publication date: 2011
https://doi.org/10.1007/978-3-642-22619-9_2
Mueen AKeogh ERao BKrishnapuram BTomkins AYang Q(2010)Online discovery and maintenance of time series motifsProceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining10.1145/1835804.1835941(1089-1098)Online publication date: 25-Jul-2010
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Arkin EBae SEfrat AOkamoto KMitchell JPolishchuk V(2009)Geometric stable roommatesInformation Processing Letters10.1016/j.ipl.2008.10.003109:4(219-224)Online publication date: 15-Jan-2009
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Sankaranarayanan JAlborzi HSamet Hde By RNittel S(2006)Distance join queries on spatial networksProceedings of the 14th annual ACM international symposium on Advances in geographic information systems10.1145/1183471.1183506(211-218)Online publication date: 10-Nov-2006
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Lenz TMitchell JRote G(2005)Reconstructing collections of arbitrary curvesProceedings of the twenty-first annual symposium on Computational geometry10.1145/1064092.1064149(366-367)Online publication date: 6-Jun-2005
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Angiulli FPizzuti C(2005)Approximate k-Closest-Pairs in Large High-Dimensional Data SetsJournal of Mathematical Modelling and Algorithms10.1007/s10852-004-4080-34:2(149-179)Online publication date: Jun-2005
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Krznaric DLevcopoulos C(2005)Optimal algorithms for complete linkage clustering in d dimensionsMathematical Foundations of Computer Science 199710.1007/BFb0029980(368-377)Online publication date: 17-Jun-2005
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Krznaric DLevcopoulos C(2002)Optimal algorithms for complete linkage clustering in d dimensionsTheoretical Computer Science10.1016/S0304-3975(01)00239-0286:1(139-149)Online publication date: 6-Sep-2002
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A New Algorithm for Finding Closest Pair of Vectors (Extended Abstract)

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A New Algorithm for Finding Closest Pair of Vectors (Extended Abstract)

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