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 π={V_B,V_W} of V with V_B∩V_W=∅, find an edge set E_f of minimum cardinality, consisting of edges that connect V_B and V_W, such that G'=(V,E∪E_f) 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}.