IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Special Section on Foundations of Computer Science — Mathematical Foundations and Applications of Computer Science and Algorithms —
A Fast Algorithm for Augmenting Edge-Connectivity by One with Bipartition Constraints
Tadachika OKISatoshi TAOKAToshiya MASHIMAToshimasa WATANABE
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Volume E95.D (2012) Issue 3 Pages 769-777

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Abstract

The k-edge-connectivity augmentation problem with bipartition constraints (kECABP, for short) is defined by “Given an undirected graph G=(V,E) and a bipartition π={VB,VW} of V with VBVW=∅, find an edge set Ef of minimum cardinality, consisting of edges that connect VB and VW, such that G'=(V,EEf) is k-edge-connected.” The problem has applications for security of statistical data stored in a cross tabulated table, and so on. In this paper we propose a fast algorithm for finding an optimal solution to (σ+1)ECABP in O(|V||E|+|V2|log |V|) time when G is σ-edge-connected (σ > 0), and show that the problem can be solved in linear time if σ ∈ {1,2}.

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© 2012 The Institute of Electronics, Information and Communication Engineers
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