Optimal point-to-point broadcast algorithms via lopsided trees

We consider the broadcasting operation in point-to-point packet-switched parallel and distributed networks of processors. We develop a general technique for the design of optimal broadcast algorithms on a wide range of such systems. The technique works by modelling broadcast algorithms using lopsided trees, i.e. trees in which different edges can have different lengths. This technique makes it easier to design such algorithms and, furthermore, provides generating function and Mellin transform tools that can be used to derive precise analyses of their running times. As direct applications of this method we give an exact analysis of a known algorithm for the POSTAL model, and design and analyze an optimal broadcast algorithm for the MULTI-PORT MULTI-MEDIA model. We then show how our method can be applied to networks with different underlying topologies, by designing and giving an exact analysis of an optimal broadcast algorithm for the OPTICAL-RING.