Broadcast-efficient algorithms on the coarse-grain broadcast communication model with few channels

The main contribution of this work is to present elegant broadcast-efficient algorithms 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 n/k broadcast rounds for any k, p, and n. We then go on to develop an on-line routing algorithm that takes 2 n/k+k-1 broadcast rounds on a p-processor, k-channel BCM, whenever k⩽√(p/2). Using this routing algorithm, we develop a ranking algorithm that takes only 3 n/k+0(n/k) broadcast rounds, as well as a sorting algorithm that takes 4 n/k+0(n/k) broadcast rounds on a p-processor, k-channel BCM, provided that k⩽√(p/2) and p∈0(n). Our algorithms offer a significant improvement over the state of the art