Euclidean movement minimization

Nima Anari (), MohammadAmin Fazli (), Mohammad Ghodsi () and MohammadAli Safari ()
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Nima Anari: University of California Berkeley
MohammadAmin Fazli: Sharif University of Technology
Mohammad Ghodsi: Sharif University of Technology
MohammadAli Safari: Sharif University of Technology

Journal of Combinatorial Optimization, 2016, vol. 32, issue 2, No 3, 354-367

Abstract: 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.

Keywords: Movement minimization; NP-hardness; Approximation algorithms (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-015-9842-5

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