Broadcast-efficient sorting in the presence of few channels

We present simple and broadcast-efficient ranking and sorting algorithms on the broadcast communication model (BCM, for short) with few communication channels. At the heart of our algorithms is a new and elegant sampling and bucketing scheme whose main feature is that the resulting buckets are well balanced, making costly rebalancing unnecessary. The resulting ranking algorithm uses only 2 n/k+o(n/k) broadcast rounds, while 3 n/k+o(n/k) broadcast rounds are needed for sorting on a L-channel, n-processor BCM whenever k⩽√(n/log n). These bounds are fairly tight, when compared with the trivial lower bound of n/k broadcast rounds necessary to permute n items using k communication channels