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A simple randomized algorithm for all nearest neighbors

Ebadian, S ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. Publisher: Canadian Conference on Computational Geometry , 2019
  3. Abstract:
  4. Given a set P of n points in the plane, the all nearest neighbors problem asks for finding the closest point in P for each point in the set. The following folklore algorithm is used for the problem in practice: Pick a line in a random direction, project all points onto the line, and then search for the nearest neighbor of each point in a small vicinity of that point on the line. It is widely believed that the expected number of points needed to be checked by the algorithm in the vicinity of each point is O(pn) on average. We confirm this conjecture in affirmative by providing a careful analysis on the expected number of comparisons made by the algorithm. We also present a matching lower bound, showing that our analysis is essentially tight. © CCCG 2019. All rights reserved
  5. Keywords:
  6. Computational geometry ; All nearest neighbors ; Lower bounds ; Nearest neighbors ; Randomized Algorithms ; Nearest neighbor search
  7. Source: 31st Canadian Conference on Computational Geometry, CCCG 2019, 8 August 2019 through 10 August 2019 ; 2019 , Pages 94-98
  8. URL: https://sites.ualberta.ca/~cccg2019/cccg2019_proceedings.pdf