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Euclidean movement minimization

Author

Listed:
  • Nima Anari

    (University of California Berkeley)

  • MohammadAmin Fazli

    (Sharif University of Technology)

  • Mohammad Ghodsi

    (Sharif University of Technology
    Institute of Research in Fundamental Sciences (IPM))

  • MohammadAli Safari

    (Sharif University of Technology)

Abstract

We consider a class of optimization problems called movement minimization on euclidean plane. Given a set of $$m$$ 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 $$O(m)$$ 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.

Suggested Citation

  • Nima Anari & MohammadAmin Fazli & Mohammad Ghodsi & MohammadAli Safari, 2016. "Euclidean movement minimization," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 354-367, August.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:2:d:10.1007_s10878-015-9842-5
    DOI: 10.1007/s10878-015-9842-5
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    Cited by:

    1. Raghavan, S. & Sahin, Mustafa & Salman, F. Sibel, 2019. "The capacitated mobile facility location problem," European Journal of Operational Research, Elsevier, vol. 277(2), pages 507-520.

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