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Scandinavian Workshop on Algorithm Theory

SWAT 1994: Algorithm Theory — SWAT '94 pp 13–24Cite as

Selection in monotone matrices and computing k th nearest neighbors

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 824))

Abstract

We present an O(m+n√n log n) time algorithm to select the k th smallest item from an m×n totally monotone matrix for any k≤mn. This is the first subquadratic algorithm for selecting an item from a totally monotone matrix. Our method also yields an algorithm for generalized row selection in monotone matrices of the same time complexity. Given a set S=p 1, ..., pn of n points in convex position and a vector k=k 1, ..., kn, we also present an O(n 4/3 logO(1) n) algorithm to compute the k thi nearest neighbor of p i for every i≤n; c is an appropriate constant. This algorithm is considerably faster than the one based on a row-selection algorithm for monotone matrices. If the points of S are arbitrary, then the k thi nearest neighbor of p i, for all i≤n, can be computed in time O(n 7/5 logc n), which also improves upon the previously best-known result.

Pankaj Agarwal has been supported by an NYI award and National Science Foundation Grant CCR-93-01259.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Duke University, PO Box 90129, 27708-0129, Durham, NC, USA

    Pankaj K. Agarwal

  2. Department of Computer Science, Indian Institute of Technology, New Delhi, India

    Sandeep Sen

Authors
  1. Pankaj K. Agarwal
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  2. Sandeep Sen
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Editor information

Erik M. Schmidt Sven Skyum

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© 1994 Springer-Verlag Berlin Heidelberg

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Agarwal, P.K., Sen, S. (1994). Selection in monotone matrices and computing k th nearest neighbors. In: Schmidt, E.M., Skyum, S. (eds) Algorithm Theory — SWAT '94. SWAT 1994. Lecture Notes in Computer Science, vol 824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58218-5_2

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  • DOI: https://doi.org/10.1007/3-540-58218-5_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58218-2

  • Online ISBN: 978-3-540-48577-3

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