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Approximate minimum diameter

Ghodsi, M ; Sharif University of Technology | 2017

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-319-62389-4_20
  3. Publisher: Springer Verlag , 2017
  4. Abstract:
  5. We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a continuous region ({Imprecise} model) or a finite set of points ({Indecisive} model). Given a set of inexact points in one of {Imprecise} or {Indecisive} models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on {Indecisive} model. We present an (formula presented) time approximation algorithm of factor (1+epsilon) for finding minimum diameter of a set of points in d dimensions. This improves the previously proposed algorithms for this problem substantially. Next, we consider the problem in {Imprecise} model. In d-dimensional space, we propose a polynomial time sqrt{d} -approximation algorithm. In addition, for d=2, we define the notion of alpha -separability and use our algorithm for {Indecisive} model to obtain (1+epsilon) -approximation algorithm for a set of alpha -separable regions in time (formula presented). © 2017, Springer International Publishing AG
  6. Keywords:
  7. Approximation algorithms ; Core-set ; Imprecise ; Indecisive ; Combinatorial mathematics ; Computational geometry ; Polynomial approximation ; Core set ; D-dimensional spaces ; Indecisive ; Lower bounds ; Minimum diameters ; Polynomial-time ; Precise locations
  8. Source: 23rd International Conference on Computing and Combinatorics, COCOON 2017, 3 August 2017 through 5 August 2017 ; Volume 10392 LNCS , 2017 , Pages 237-249 ; 03029743 (ISSN); 9783319623887 (ISBN)
  9. URL: https://link.springer.com/chapter/10.1007/978-3-319-62389-4_20