The subject of the paper is to propose a simple O(|V|+|E|) algorithm for finding all 3-edge-components of a given undirected multigraph G=(V, E). An 3-edge-connected component of G is defined as a maximal set of vertices such that G has at least three edge-disjoint paths between every pair of vertices in the set. The algorithm is based on the depth-first search (DFS) technique. For any fixed DFS-tree T of G, cutpairs of G are partitioned into two types: a type 1 pair consists of an edge of T and a back edge; a type 2 pair consists of two edges of T. All type 1 pairs can easily be determined in O(|V|+|E|) time. The point is that an edge set KE(T) in which any type 2 pair is included can be found in O(|V|+|E|) time. All 3-edge-components of G appear as connected components if we delete from G all edges contained in type 1 pairs or in the edge set KE(T).

We describe two information disseminating schemes, t-disseminate and t-Rdisseminate in a computer network with N processors, where each processor can send a message to t-directions at each round. If no processors have failed, these schemes are time optimal. When at most t processors have failed, for t1 and t2 any of these schemes can broadcast information within any consecutive logt+1N2 rounds, and for an arbitrary t they can broadcast information within any consecutive logt+1N3 rounds.