The Relationship Between Gossiping in Vertex-Disjoint Paths Mode and Bisection Width

The two-way communication mode used for sending messages to processors of interconnection networks via vertex-disjoint paths in one communication step is investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). This paper establishes a direct relationship between the gossip complexity and the vertex bisection width. More precisely, the main results are the following: 1. The lower bound 2 log2n − log2k − log2 log2k − 2 is proved on the number of rounds of every two-way gossip algorithm working on any graph Gn,k of n nodes and vertex bisection k. 2. A graph Gn,k of n nodes and vertex bisection k, and a two-way gossip algorithm for Gn,k is constructed working in 2 log2n − log2k −log2 log2k + 2 rounds.