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Minimum Weight Connectivity Augmentation for Planar Straight-Line Graphs

  • Hugo A. Akitaya
  • Rajasekhar Inkulu
  • Torrie L. Nichols
  • Diane L. Souvaine
  • Csaba D. Tóth
  • Charles R. Winston
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10167)

Abstract

We consider edge insertion and deletion operations that increase the connectivity of a given planar straight-line graph (PSLG), while minimizing the total edge length of the output. We show that every connected PSLG \(G=(V,E)\) in general position can be augmented to a 2-connected PSLG \((V,E\cup E^+)\) by adding new edges of total Euclidean length \(\Vert E^+\Vert \le 2\Vert E\Vert \), and this bound is the best possible. An optimal edge set \(E^+\) can be computed in \(O(|V|^4)\) time; however the problem becomes NP-hard when G is disconnected. Further, there is a sequence of edge insertions and deletions that transforms a connected PSLG \(G=(V,E)\) into a plane cycle \(G'=(V,E')\) such that \(\Vert E'\Vert \le 2\Vert \mathrm{MST}(V)\Vert \), and the graph remains connected with edge length below \(\Vert E\Vert +\Vert \mathrm{MST}(V)\Vert \) at all stages. These bounds are the best possible.

Keywords

Span Tree Edge Incident Delaunay Triangulation Simple Cycle Unit Disk Graph 
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 International Publishing AG 2017

Authors and Affiliations

  • Hugo A. Akitaya
    • 1
  • Rajasekhar Inkulu
    • 2
  • Torrie L. Nichols
    • 3
  • Diane L. Souvaine
    • 1
  • Csaba D. Tóth
    • 1
    • 3
  • Charles R. Winston
    • 1
  1. 1.Tufts UniversityMedfordUSA
  2. 2.Indian Institute of Technology GuwahatiGuwahatiIndia
  3. 3.California State University NorthridgeLos AngelesUSA

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