Journal of Combinatorial Optimization

, Volume 32, Issue 2, pp 354–367 | Cite as

Euclidean movement minimization

  • Nima Anari
  • MohammadAmin Fazli
  • Mohammad Ghodsi
  • MohammadAli Safari
Article
  • 176 Downloads

Abstract

We consider a class of optimization problems called movement minimization on euclidean plane. Given a set of \(m\) nodes on the plane, the aim is to achieve some specific property by minimum movement of the nodes. We consider two specific properties, namely the connectivity (Con) and realization of a given topology (Topol). By minimum movement, we mean either the sum of all movements (Sum) or the maximum movement (Max). We obtain several approximation algorithms and some hardness results for these four problems. We obtain an \(O(m)\)-factor approximation for ConMax and ConSum and extend some known result on graphical grounds and obtain inapproximability results on the geometrical grounds. For the Topol problems (where the final decoration of the nodes must correspond to a given configuration), we find it much simpler and provide FPTAS for both Max and Sum versions.

Keywords

Movement minimization NP-hardness Approximation algorithms 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Nima Anari
    • 1
  • MohammadAmin Fazli
    • 2
  • Mohammad Ghodsi
    • 2
    • 3
  • MohammadAli Safari
    • 2
  1. 1.Computer Science DivisionUniversity of California BerkeleyBerkeleyUSA
  2. 2.Department of Computer EngineeringSharif University of TechnologyTehranIran
  3. 3.Institute of Research in Fundamental Sciences (IPM)TehranIran

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