1 research outputs found
Minimal contention-free matrices with application to multicasting
In this paper, we show that the multicast problem in trees can be
expressed in term of arranging rows and columns of boolean matrices.
Given a matrix with 0-1 entries, the {\em shadow}
of is defined as a boolean vector of entries such that
if and only if there is no 1-entry in the th column of
, and otherwise. (The shadow can also be seen as the
binary expression of the integer .
Similarly, every row of can be seen as the binary expression of
an integer.) According to this formalism, the key for solving a
multicast problem in trees is shown to be the following. Given a matrix with 0-1 entries, finding a matrix such
that:
1- has at most one 1-entry per column;
2- every row of (viewed as the binary expression of
an integer) is larger than the corresponding row of , ; and
3- the shadow of (viewed as an integer) is minimum.
We show that there is an algorithm that
returns for any boolean matrix .
The application of this result is the following: Given a {\em directed}
tree whose arcs are oriented from the root toward the leaves,
and a subset of nodes , there exists a polynomial-time algorithm
that computes an optimal multicast protocol from the root to all
nodes of in the all-port line model.Peer Reviewe