Edge-connectivity augmentation problems
Journal of Computer and System Sciences
Journal of Algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
A 5/4-approximation algorithm for minimum 2-edge-connectivity
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Factor 4/3 approximations for minimum 2-connected subgraphs
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Independence free graphs and vertex connectivity augmentation
Journal of Combinatorial Theory Series B
Augmenting the connectivity of geometric graphs
Computational Geometry: Theory and Applications
Planar subgraphs without low-degree nodes
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Approximating the edge length of 2-edge connected planar geometric graphs on a set of points
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Hi-index | 0.02 |
Algorithms for the construction of spanning planar subgraphs of Unit Disk Graphs (UDGs) do not ensure connectivity of the resulting graph under single edge deletion. To overcome this deficiency, in this paper we address the problem of augmenting the edge set of planar geometric graphs with straight line edges of bounded length so that the resulting graph is planar and 2-edge connected. We give bounds on the number of newly added straight-line edges and show that such edges can be of length at most 3 times the max length of the edges of the original graph; also 3 is shown to be optimal. It is shown to be NP-hard to augment a geometric planar graph to a 2-edge connected geometric planar with the minimum number of new edges of a given bounded length. Further, we prove that there is no local algorithm for augmenting a planar UDG into a 2-edge connected planar graph with straight line edges.