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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
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7846)

Abstract

We study optimization problems for the Euclidean minimum spanning tree (MST) 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 (\(\textsc{MSTN}\)) problem, and the maximum weight version (\(\textsc{max-MSTN}\)) has not been studied previously to our knowledge. We provide deterministic and parameterized approximation algorithms for the \(\textsc{max-MSTN}\) problem, and a parameterized algorithm for the \(\textsc{MSTN}\) problem. Additionally, we present hardness of approximation proofs for both settings.

Keywords

Tangent Point Satisfying Assignment Minimum Span Tree Problem Variable Gadget Disjoint Disk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

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

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