Theory of Computing Systems

, Volume 56, Issue 1, pp 220–250 | Cite as

On Minimum- and Maximum-Weight Minimum Spanning Trees with Neighborhoods

  • Reza Dorrigiv
  • Robert Fraser
  • Meng He
  • Shahin Kamali
  • Akitoshi Kawamura
  • Alejandro López-Ortiz
  • Diego Seco
Article

Abstract

We study optimization problems for the Euclidean Minimum Spanning Tree (MST) problem on imprecise data. To model imprecision, we accept a set of disjoint disks in the plane as input. From each member of the set, one point must be selected, and the MST is computed over the set of selected points. We consider both minimizing and maximizing the weight of the MST over the input. The minimum weight version of the problem is known as the Minimum Spanning Tree with Neighborhoods (MSTN) problem, and the maximum weight version (max-MSTN) has not been studied previously to our knowledge. We provide deterministic and parameterized approximation algorithms for the max-MSTN problem, and a parameterized algorithm for the MSTN problem. Additionally, we present hardness of approximation proofs for both settings.

Keywords

Computational geometry Imprecise data Minimum spanning trees 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Reza Dorrigiv
    • 1
  • Robert Fraser
    • 2
  • Meng He
    • 1
  • Shahin Kamali
    • 3
  • Akitoshi Kawamura
    • 4
  • Alejandro López-Ortiz
    • 3
  • Diego Seco
    • 5
  1. 1.Dalhousie UniversityHalifaxCanada
  2. 2.University of ManitobaWinnipegCanada
  3. 3.University of WaterlooWaterlooCanada
  4. 4.University of TokyoTokyoJapan
  5. 5.University of ConcepciónConcepciónChile

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