A Parallel Algorithm for 2-Edge-Connectivity Augmentation of a Connected Graph with Multipartition Constraints

The k-edge-connectivity augmentation problem with multipartition constraints (kECAM for short) is defined by “Given an undirected graph G = (V, E) and a multipartition π = {V
₁
,..., V
_r
} of V with V
_i
∩ V
_j
= 0 for ∀i, j ∈ {1,..., r} (i ≠ j), find an edge set E' of minimum cardinality, consisting of edges that connect distinct members of π, such that G' = (V, E∪E') is k edge-connected.” In this paper, we propose a parallel algorithm, running on an EREW PRAM, for finding a solution to 2ECAM when G is connected. The main idea is to reduce 2ECAM to the bipartition case, that is, 2ECAM with r = 2.