Article

Reductions among high dimensional proximity problems

Authors:

Kasturi VaradarajanAuthors Info & Claims

SODA '01: Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms

Pages 769 - 778

Published: 09 January 2001 Publication History

Abstract

We present improved running times for a wide range of approximate high dimensional proximity problems. We obtain subquadratic running time for each of these problems. These improved running times are obtained by reduction to Nearest Neighbour queries. The problems we consider in this paper are Approximate Diameter, Approximate Furthest Neighbours, Approximate Discrete Center, Approximate Metric Facility Location, Approximate Bottleneck Matching, and Approximate Minimum Weight Matching.

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Cited By

Avarikioti GEmiris IKavouras LPsarros IKlein P(2017)High-dimensional approximate r-netsProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039688(16-30)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039688
Pagh RSilvestri FSivertsen JSkala M(2017)Approximate furthest neighbor with application to annulus queryInformation Systems10.1016/j.is.2016.07.00664:C(152-162)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.is.2016.07.006
Har-Peled SKumar NMount DRaichel B(2016)Space Exploration via Proximity SearchDiscrete & Computational Geometry10.1007/s00454-016-9801-756:2(357-376)Online publication date: 1-Sep-2016
https://dl.acm.org/doi/10.1007/s00454-016-9801-7
Show More Cited By

Index Terms

Reductions among high dimensional proximity problems
1. Mathematics of computing
  1. Discrete mathematics
  2. Mathematical analysis
    1. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
  2. Randomness, geometry and discrete structures

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Published In

cover image ACM Conferences

SODA '01: Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms

January 2001

937 pages

ISBN:0898714907

Chairman:
S. Rao Kosaraju

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIAM: Society for Industrial and Applied Mathematics

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 09 January 2001

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

Avarikioti GEmiris IKavouras LPsarros IKlein P(2017)High-dimensional approximate r-netsProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039688(16-30)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039688
Pagh RSilvestri FSivertsen JSkala M(2017)Approximate furthest neighbor with application to annulus queryInformation Systems10.1016/j.is.2016.07.00664:C(152-162)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.is.2016.07.006
Har-Peled SKumar NMount DRaichel B(2016)Space Exploration via Proximity SearchDiscrete & Computational Geometry10.1007/s00454-016-9801-756:2(357-376)Online publication date: 1-Sep-2016
https://dl.acm.org/doi/10.1007/s00454-016-9801-7
Agarwal PSharathkumar R(2015)Streaming Algorithms for Extent Problems in High DimensionsAlgorithmica10.1007/s00453-013-9846-472:1(83-98)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1007/s00453-013-9846-4
Pagh RSilvestri FSivertsen JSkala M(2015)Approximate Furthest Neighbor in High DimensionsProceedings of the 8th International Conference on Similarity Search and Applications - Volume 937110.1007/978-3-319-25087-8_1(3-14)Online publication date: 12-Oct-2015
https://dl.acm.org/doi/10.1007/978-3-319-25087-8_1
Agarwal PSharathkumar RShmoys D(2014)Approximation algorithms for bipartite matching with metric and geometric costsProceedings of the forty-sixth annual ACM symposium on Theory of computing10.1145/2591796.2591844(555-564)Online publication date: 31-May-2014
https://dl.acm.org/doi/10.1145/2591796.2591844
Arya SChan TCheng SDevillers O(2014)Better ϵ-Dependencies for Offline Approximate Nearest Neighbor Search, Euclidean Minimum Spanning Trees, and ϵ-KernelsProceedings of the thirtieth annual symposium on Computational geometry10.1145/2582112.2582161(416-425)Online publication date: 8-Jun-2014
https://dl.acm.org/doi/10.1145/2582112.2582161
Munteanu ASohler CFeldman DCheng SDevillers O(2014)Smallest enclosing ball for probabilistic dataProceedings of the thirtieth annual symposium on Computational geometry10.1145/2582112.2582114(214-223)Online publication date: 8-Jun-2014
https://dl.acm.org/doi/10.1145/2582112.2582114
Lee ESchulman LKhanna S(2013)Clustering affine subspacesProceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms10.5555/2627817.2627875(810-827)Online publication date: 6-Jan-2013
https://dl.acm.org/doi/10.5555/2627817.2627875
Larsson TKällberg LFalcidieno BSpagnuolo MLipman YZhang H(2013)Fast and robust approximation of smallest enclosing balls in arbitrary dimensionsProceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing10.5555/2600289.2600303(93-101)Online publication date: 3-Jul-2013
https://dl.acm.org/doi/10.5555/2600289.2600303
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