TY - GEN

T1 - Compatible connectivity-augmentation of planar disconnected graphs

AU - Aloupis, Greg

AU - Barba, Luis

AU - Carmi, Paz

AU - Dujmović, Vida

AU - Frati, Fabrizio

AU - Morin, Pat

N1 - Publisher Copyright:
Copyright © 2015 by the Society for Industrial and Applied Mathmatics.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Motivated by applications to graph morphing, we consider the following compatible connectivity-augmentation problem: We are given a labelled n-vertex planar graph, Q, that has τ ≥ 2 connected components, and k ≥ 2 isomorphic planar straight-line drawings, G1,⋯ ,Gk, of Q. We wish to augment Q by adding vertices and edges to make it connected in such a way that these vertices and edges can be added to G1⋯Gk as points and straight-line segments, respectively, to obtain k planar straight-line drawings isomorphic to the augmentation of Q. We show that adding θ (nr1-1/k) edges and vertices to Q is always sufficient and sometimes necessary to achieve this goal. The upper bound holds for all τ ∈ {2⋯ n} and k ≥ 2 and is achievable by an algorithm whose running time is θ (nr1-1/k) for k = O (l) and whose running time is 0 (kn2) for general values of k. The lower bound holds for all τ ∈ {2,⋯, n/4} and k ≥ 2.

AB - Motivated by applications to graph morphing, we consider the following compatible connectivity-augmentation problem: We are given a labelled n-vertex planar graph, Q, that has τ ≥ 2 connected components, and k ≥ 2 isomorphic planar straight-line drawings, G1,⋯ ,Gk, of Q. We wish to augment Q by adding vertices and edges to make it connected in such a way that these vertices and edges can be added to G1⋯Gk as points and straight-line segments, respectively, to obtain k planar straight-line drawings isomorphic to the augmentation of Q. We show that adding θ (nr1-1/k) edges and vertices to Q is always sufficient and sometimes necessary to achieve this goal. The upper bound holds for all τ ∈ {2⋯ n} and k ≥ 2 and is achievable by an algorithm whose running time is θ (nr1-1/k) for k = O (l) and whose running time is 0 (kn2) for general values of k. The lower bound holds for all τ ∈ {2,⋯, n/4} and k ≥ 2.

UR - http://www.scopus.com/inward/record.url?scp=84938228774&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973730.106

DO - 10.1137/1.9781611973730.106

M3 - Conference contribution

AN - SCOPUS:84938228774

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1602

EP - 1615

BT - Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

PB - Association for Computing Machinery

T2 - 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

Y2 - 4 January 2015 through 6 January 2015

ER -