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Improved selection in totally monotone arrays

  • Yishay Mansour
  • James K. Park
  • Baruch Schieber
  • Sandeep Sen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 560)

Abstract

This paper's main result is an O((√m lg m)(n lg n)+m lg n)-time algorithm for computing the kth smallest entry in each row of an m×n totally monotone array. (A two-dimensional array A = {a[i,j]} is totally monotone if for all i1<i2 and j1<j2, a[i1,j1]<a[i1,j2] implies a[i2,j1<a[i2,j2.) For large values of k (in particular, for k=[n/2]), this algorithm is significantly faster than the O(k(m+n))-time algorithm for the same problem due to Kravets and Park (1991). An immediate consequence of this result is an O(n3/2 lg2n)-time algorithm for computing the kth nearest neighbor of each vertex of a convex n-gon. In addition to the main result, we also give an O(n lg m)-time algorithm for computing an approximate median in each row of an m×n totally monotone array; this approximate median is an entry whose rank in its row lies between [n/4] and [3n/4].

Keywords

Time Algorithm Linear Time Algorithm Watson Research 29th Annual IEEE Symposium Median Entry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Yishay Mansour
    • 1
  • James K. Park
    • 2
  • Baruch Schieber
    • 3
  • Sandeep Sen
    • 3
  1. 1.Aiken Computation LaboratoryHarvard UniversityCambridge
  2. 2.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridge
  3. 3.IBM Research DivisionT. J. Watson Research CenterYorktown Heights

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