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Efficient broadcasting from several originators in a d\Gamma dimensional grid

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 ([11] 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
different originators.
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 [5] , Van­Scoy and Brooks [12] and Roditty and Shoham [10].
\Lambda Department of Computer Science, School of Mathematical Sciences, Tel Aviv Univer­
sity, Tel Aviv 69978, Israel.


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences