Two-Vertex Connectivity Augmentations for Graphs with a Partition Constraint (Extended Abstract)

Authors:
Pei-Chi Huang;Hsin-Wen Wei;Yen-Chiu Chen;Ming-Yang Kao;Wei-Kuan Shih;Tsan-Sheng Hsu
Affiliations:
Department of Computer Science, National Tsing-Hua University, Taiwan;Institute of Information Science, Academia Sinica, Taiwan;Department of Computer Science, National Tsing-Hua University, Taiwan;Department of Electrical Engineering and Computer Science, Northwestern University, U.S.A.;Department of Computer Science, National Tsing-Hua University, Taiwan;Institute of Information Science, Academia Sinica, Taiwan
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

In this paper, we study the two-vertex connectivity augmentation problem in an undirected graph whose vertices are partitioned into k sets. Our objective is to add the smallest number of edges to the graph such that the resulting graph is 2-vertex connected under the constraint that each new edge is between two different sets in the partition. We propose an algorithm to solve the above augmentation problem that runs in linear time in the size of the input graph.