The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. In this paper, we consider the parallel complexity of two matrix problems: Gaussian elimination with pairwise pivoting, and orthogonal matrix decomposition by Givens rotations. We define a common framework that unifies both problems, and present a new communication-efficient BSP algorithm for their solution. Apart from being a useful addition to the growing collection of efficient BSP algorithms, our result can be viewed as a refinement of the classical "parallelism-communication tradeoff". © Springer-Verlag Berlin Heidelberg 2003.