Broadcast-Efficient Algorithms on the Coarse-Grain Broadcast Communication Model with Few Channels

The main contribution of this work is to present elegant broadcast-efficientalgorithms for permutation routing, ranking, and sorting n items on the Broadcast Communication Model (BCM, for short) endowed with p processors and k communication channels. We begin by presenting an optimal off-line routing algorithm using nk broadcast rounds for any k, p, and n. We then go on to develop an on-line routing algorithm that takes 2nk + k 1 broadcast rounds on a p-processor, k-channel BCM, whenever k p p2 . Using this routing algorithm, we develop a ranking algorithm that takes only 3nk + o( n k ) broadcast rounds, as well as a sorting algorithm that takes 4nk +o( n k ) broadcast rounds on a p-processor, k-channel BCM, provided that k p p2 and p 2 o(n). Our algorithms offer a significant improvement over the state of the art.