The Bridge-connectivity Augmentation Problem with a partition Constraint

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Title:	The Bridge-connectivity Augmentation Problem with a partition Constraint
Authors:	Chen, Yen-Chiu;Wei, Hsin-Wen;Huang, Pei-Chi;Shih, Wei-Kuan;Hsu, Tsan-sheng
Contributors:	淡江大學電機工程學系
Keywords:	2-edge-connectivity;Bridge-connectivity;Augmentation;Partition constraint
Date:	2010-06
Issue Date:	2014-03-03 16:19:35 (UTC+8)
Publisher:	Amsterdam: Elsevier BV
Abstract:	In this paper, we consider the augmentation problem of an undirected graph with k partitions of its vertices. The main issue is how to add a set of edges with the smallest possible cardinality so that the resulting graph is 2-edge-connected, i.e., bridge-connected, while maintaining the original partition constraint. To solve the problem, we propose a simple linear-time algorithm. To the best of our knowledge, the most efficient sequential algorithm runs in O(n(m+nlogn)logn) time. However, we show that it can also run in O(logn) parallel time on an EREW PRAM using a linear number of processors, where n is the number of vertices in the input graph. If a simple graph exists, our main algorithm ensures that it is as simple as possible.
Relation:	Theoretical Computer Science 411(31–33), pp.2878–2889
DOI:	10.1016/j.tcs.2010.04.019
Appears in Collections:	[Graduate Institute & Department of Electrical Engineering] Journal Article

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