Compatible Connectivity Augmentation of Planar Disconnected Graphs

Greg Aloupis, Luis Barba, Paz Carmi, Vida Dujmović, Fabrizio Frati, Pat Morin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the following compatible connectivity-augmentation problem: We are given a labeled n-vertex planar graph $G that has r≥2 connected components, and k≥2 isomorphic plane straight-line drawings (Formula presented.) of G. We wish to augment G by adding vertices and edges to make it connected in such a way that these vertices and edges can be added to (Formula presented.) as points and straight line segments, respectively, to obtain k plane straight-line drawings isomorphic to the augmentation of G. We show that adding (Formula presented.) edges and vertices to G is always sufficient and sometimes necessary to achieve this goal. The upper bound holds for all r∈{2,…,n} and k≥2 and is achievable by an algorithm whose running time is (Formula presented.) for k=O(1) and whose running time is (Formula presented.) for general values of k. The lower bound holds for all r∈{2,…,n/4} and k≥2.

Original languageAmerican English
Pages (from-to)459-480
Number of pages22
JournalDiscrete and Computational Geometry
Volume54
Issue number2
DOIs
StatePublished - 27 Sep 2015

Keywords

  • Connectivity
  • Euclidean minimum spanning trees
  • Graph drawing
  • Planar graphs

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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