The Relationship Between Gossiping inVertex - Disjoint Paths Mode

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 log 2 n ? log 2 k ? log 2 log 2 k ? 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 log 2 n?log 2 k? log 2 log 2 k + 2 rounds. The second result shows that this improvement is the best possible with respect to the class of all graphs Gn;k of n nodes and vertex bisection k.