Approximation and heuristic algorithms for minimum delay application-layer multicast trees

We investigate the problem of finding the minimum delay application-layer multicast trees, such as the trees constructed in overlay networks. It is accepted that shortest path trees are not a good solution for the problem since such trees can have nodes with very large degree, termed high load nodes. The load on these nodes makes them a bottleneck in the distribution tree, due to computation load and access link bandwidth constrains. Many previous solutions limited the maximal degree of the nodes by introducing arbitrary constraints. In this work, we show how to directly map the node load to the delay penalty at the application host, and create a new model that captures the trade offs between the desire to select shortest path trees and the need to constrain the load on the hosts. In this model the problem is shown to be NP-hard. Therefore, we present a logarithmic approximation algorithm and an alternative heuristic solution. Our heuristic algorithm is shown by simulations to be scalable for large group sizes, and produces results that are very close to optimal.