In this paper we implement several basic operating system primitives by using a "replace-add" operation, which can supersede the standard "test and set", and which appears to be a universal primitive for efficiently coordinating large numbers of independently acting sequential processors. We also present a hardware implementation of replace-add that permits multiple replace-adds to be processed nearly as efficiently as loads and stores. Moreover, the crucial special case of concurrent replace-adds updating the same variable is handled particularly well: If every PE simultaneously addresses a replace-add at the same variable, all these requests are satisfied in the time required to process just one request.

Hypercube algorithms are developed for a variety of communication-intensive tasks such as transposing a matrix, histogramming, one node sending a (long) message to another, broadcasting a message from one node to all others, each node broadcasting a message to all others, and nodes exchanging messages via a fixed permutation. The algorithm for exchanging via a fixed permutation can be viewed as a deterministic analogue of Valiant's randomized routing. The algorithms are for link-bound hypercubes in which local processing time is ignored, communication time predominates, message headers are not needed because all nodes know the task being performed, and all nodes can use all communication links simultaneously. Through systematic use of techniques such as pipelining, batching, variable packet sizes, symmetrizing, and completing, for all problems algorithms are obtained which achieve a time with an optimal highest-order term. 1 Introduction This paper gives efficient hypercube algorith...

We discuss the problem of routing messages on hypercubes which have faulty processors and/or communication links. We are motivated by the belief that simple algorithms, operating under simple assumptions, can ensure high probabilities of successful message routing. In this paper, we consider the basic problem of routing a single message from an arbitrary source to an arbitrary destination. In our study, a fault is assumed to render the processor or link non-functional for purposes of communicating messages. As such, we may also consider communications hot spots as node faults, and our results also apply to routing in congested hypercubes. A framework for the analysis of fault tolerant routing schemes on a hypercube is presented. This framework includes differing routing schemes, routing information models and fault distribution models. The a priori probabilities of successful routing of a single, indivisible message under each of our possible sets of assumptions are calculated. Using random routing, under the one-step local information routing model, we show that the a priori probability of successful message routing is high even for an exceedingly large number of faults. We also analyze the behavior of sidetracking, a routing method which combines the concepts of local information and randomization. Using sidetracking, and in the one-step local information routing model,