Summary: Efficient broadcasting from several originators
in a d\Gamma dimensional grid
A. Averbuch \Lambda I. Gaber y Y. Roditty z
Given an undirected graph representing a network of processors,
and source nodes (called originators) containing messages that must
be broadcast to all other nodes we want to find a scheme that ac
complishes the task in as small number of time steps as possible. The
general problem is known to be NPcomplete ( unless the structure
of the graph is known in advance. Let G be a d\Gammadimensional grid, and
let f(d; k) be the time needed to broadcast one message in G from k
Our main results are:
1. Exact values of f(1; k)
2. Optimal bounds on f(2; k)
3. Bounds on f(d; k).
The results are extensions of earlier results of Farley and Hedet
niemi  , VanScoy and Brooks  and Roditty and Shoham .
\Lambda Department of Computer Science, School of Mathematical Sciences, Tel Aviv Univer
sity, Tel Aviv 69978, Israel.