Broadcasting in hypercubes in the circuit switched model

Abstract

In this paper, we propose a method which enables us to construct almost optimal broadcast schemes on an n-dimensional hypercube in the circuit switched, -port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured by a flow technique and results about symmetric flow networks.We apply the method to design new schemes improving and generalizing the previous results. Our schemes are the best possible algebraic schemes, and they are optimal in the case n = 2 p , 1.

All-port line broadcasting in highly connected graphs

“…In a cycle, which is 2-edge connected, there is clearly a log 3 n time protocol. Also, the conjecture was proven to be true for two-dimensional toroidal grids [11] and for hypercubes [1].…”

“…However, it was shown that finding an optimum broadcasting protocol given a general graph is NP-complete [4]. As for specific topologies, efficient protocols were given for trees [3], torus networks [11] and hypercubes [1].…”

Rooted level-disjoint partitions of Cartesian products

“…T S (2, 10) (5, 1) (6, 2) (9, 5) (10, 6) (1,9) (2, 10) (5, 1) (6, 2) (9, 5) (10, 6) (1,9) (3, 11) (4, 0) ( …”