A fast algorithm for augmenting edge-connectivity by one with bipartition constraints

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 φ = {VB, VW} of V with VB U VW = π, find an edge set Ef of minimum cardinality, consisting of edges that connect VB and VW, such that G' = (V, E Ef ) 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 ε {1, 2}. Copyright © 2012 The Institute of Electronics, Information and Communication Engineers.