The k-edge-connectivity augmentation problem with multipartition constraints (kECAMP, for short) is defined by “Given a multigraph G=(V,E) and a multipartition π={V1,...,Vr} (r≥2) of V, that is, $V = igcup_{h = 1}^r V_h$ and Vi∩Vj=∅ (1≤i

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 VB ∩ VW = ∅, 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 ∈ {1, 2}.