In this paper we prove time and space bounds for the implementation of the programming language NESL on various parallel machine models. NESL is a sugared typed J-calculus with a set of array primitives and an explicit parallel map over arrays. Our results extend previous work on provable implementation bounds for functional languages by considering space and by including arrays. For modeling the cost of NESL we augment a standard call-by-value operational semantics to return two cost measures: a DAG representing the sequential dependence in the computation, and a measure of the space taken by a sequential implementation. We show that a NESL program with w work (nodes in the DAG), d depth (levels in the DAG), and s sequential space can be implemented on a p processor butterfly network, hypercube, or CRCW PRAM usin O(w/p + d log p) time and 0(s + dp logp) reachable space. For programs with sufficient parallelism these bounds are optimal in that they give linew speedup and use space within a constant factor of the sequential space. 1

Speculative evaluation, including leniency and futures, is often used to produce high degrees of parallelism. Existing speculative implementations, however, may serialize computation because of their implementation of queues of suspended threads. We give a provably efficient parallel implementation of a speculative functional language on various machine models. The implementation includes proper parallelization of the necessary queuing operations on suspended threads. Our target machine models are a butterfly network, hypercube, and PRAM. To prove the efficiency of our implementation, we provide a cost model using a profiling semantics and relate the cost model to implementations on the parallel machine models. 1 Introduction Futures, lenient languages, and several implementations of graph reduction for lazy languages all use speculative evaluation (call-by-speculation [15]) to expose parallelism. The basic idea of speculative evaluation, in this context, is that the evaluation of a...

We show that simulating a step of a fetch&add pram model on an erew pram model can be made as efficient as integer sorting. In particular, we present several efficient reductions of the simulation problem to various integer sorting problems. By using some recent algorithms for integer sorting, we get simulation algorithms on crew and erew that take o(n lg n) operations where n is the number of processors in the simulated crcw machine. Previous simulations were using \Theta(n lg n) operations. Some of the more interesting simulation results are obtained by using a bootstrapping technique with a crcw pram algorithm for hashing. 1 Introduction The concurrent-read concurrent-write (crcw) pram programmer's model is commonly used for designing parallel algorithms. On the other hand, the weaker exclusive-write pram models are sometimes considered closer to realization. Therefore, while it is more convenient to design algorithms for the stronger crcw model, an extra effort is sometimes neede...

A hash table is a representation of a set in a linear size data structure that supports constanttime membership queries. We show how to construct a hash table for any given set of n keys in O(lg lg n) parallel time with high probability, using n processors on a weak version of a crcw pram. Our algorithm uses a novel approach of hashing by "oblivious execution" based on probabilistic analysis to circumvent the parity lower bound barrier at the near-logarithmic time level. The algorithm is simple and is sketched by the following: 1. Partition the input set into buckets by a random polynomial of constant degree. 2. For t := 1 to O(lg lg n) do (a) Allocate M t memory blocks, each of size K t . (b) Let each bucket select a block at random, and try to injectively map its keys into the block using a random linear function. Buckets that fail carry on to the next iteration. The crux of the algorithm is a careful a priori selection of the parameters M t and K t . The algorithm uses only O(lg lg...

Multiprocessor scheduling in a shared multiprogramming environment is often structured as two-level scheduling, where a kernellevel job scheduler allots processors to jobs and a user-level task scheduler schedules the work of a job on the allotted processors. In this context, the number of processors allotted to a particular job may vary during the job’s execution, and the task scheduler must adapt to these changes in processor resources. For overall system efficiency, the task scheduler should also provide parallelism feedback to the job scheduler to avoid the situation where a job is allotted processors that it cannot use productively. We present an adaptive task scheduler for multitasked jobs with dependencies that provides continual parallelism feedback to the job scheduler in the form of requests for processors. Our scheduler guarantees that a job completes near optimally while utilizing at least a constant fraction of the allotted processor cycles. Our