Center-based broadcasting

We consider the problem of routing broadcast messages in a loosely-coupled store-and-forward network like the ARPANET. Dalal discussed a solution to this problem that minimizes the cost of a broadcast; in contrast, we are interested in performing broadcast with small delay. Existing algorithms can minimize the delay but seem unsuitable for use in a distributed environment because they involve a high degree of overhead in the form of redundant messages or data-structure space. We propose the schemes of center-based forwarding; the routing of all broadcasts via the shortest-path tree for some selected node called the center. These algorithms have small delay and also are easy to implement in a distributed system. To evaluate center-based forwarding, we define four measures of the delay associated with a given broadcast mechanism, and then propose three ways of selecting a center node. For each of the three forms of center-based forwarding we compare the delay to the minimum delay for any broadcasting scheme and also to the minimum delay for any single tree. In most cases, a given measure of the delay on the centered tree is bounded by a small constant factor relative to either of these two minimum delays. When it is possible, we give a tight bound on the ratio between the center-based delay and the minimum delay; otherwise we demonstrate that no bound is possible. These results give corollary bounds on how bad the three centered trees can be with respect to each other; most of these bounds are immediately tight, and the rest are replaced by better bounds that are also shown to be tight.