Tree Layout for Internal Network Characterizations in Multicast Networks

Abstract

There has been considerable activity recently to develop monitoring and debugging tools for a multicast session (tree). With these tools in mind, we focus on the problem of how to lay out multicast sessions so as to cover a set of links of interest within a network. We define two variations of this layout (cover)problems that differ in what it means for a link to be covered. We then focus on the minimum cost problem, to determine the minimum cost set of trees that cover the links in question. We show that, with few exceptions, the minimum cost problems are NP-hard and that even finding an approximation within a certain factor is NP-hard. One exception is when the underlying network topology is a tree. For this case, we demonstrate an efficient algorithm that finds the optimal solution. We also present several computationally efficient heuristics and their evaluation through simulation. We find that two heuristics, a greedy heuristic that combines sets of trees with three or fewer receivers, and a heuristic based on our tree algorithm, both perform reasonably well. The remainder of the paper applies our techniques to the vBNS network and randomly generated networks, examining the effectiveness of the different heuristics.

This work is sponsored in part by the DARPA and Air Force Research Laboratory under agreement F30602-98-2-0238.