Very Efficient Cyclic Shifts on Hypercubes

Abstract

Cyclic shifts are intrinsic operations in many parallel algorithms. Therefore, it is important to execute them efficiently. In this note, we present and analyze an algorithm for the cyclic shift operation onn-dimensional (distributed memory) hypercubes. On asynchronous hypercubes, we have shown that all previously known algorithms for cyclic shifts need local message buffers. In order to overcome this, we present an algorithm that always uses link-disjoint paths for routing. We prove that by using this algorithm, any cyclic shift can be realized by using at most 4/3nsteps, without using any local message buffers.