This paper studies the problem of efficiently scheduling fully strict (i.e., well-structured) multithreaded computations on parallel computers. A popular and practical method of scheduling this kind of dynamic MIMD-style computation is "work stealing," in which processors needing work steal computational threads from other processors. In this paper, we give the first provably good work-stealing scheduler for multithreaded computations with dependencies. Specifically,

Many parallel algorithms are naturally expressed at a fine level of granularity, often finer than a MIMD parallel system can exploit efficiently. Most builders of parallel systems have looked to either the programmer or a parallelizing compiler to increase the granularity of such algorithms. In this paper we explore a third approach to the granularity problem by analyzing two strategies for combining parallel tasks dynamically at run-time. We reject the simpler load-based inlining method, where tasks are combined based on dynamic load level, in favor of the safer and more robust lazy task creation method, where tasks are created only retroactively as processing resources become available. These strategies grew out of work on Mul-T [15], an efficient parallel implementation of Scheme, but could be used with other languages as well. We describe our Mul-T implementations of lazy task creation for two contrasting machines, and present performance statistics which show the method's effectiveness. Lazy task creation allows efficient execution of naturally expressed algorithms of a substantially finer grain than possible with previous parallel Lisp systems.

. This paper considers the problem of scheduling dynamic parallel computations to achieve linear speedup without using significantly more space per processor than that required for a single-processor execution. Utilizing a new graph-theoretic model of multithreaded computation, execution efficiency is quantified by three important measures: T 1 is the time required for executing the computation on 1 processor, T1 is the time required by an infinite number of processors, and S 1 is the space required to execute the computation on 1 processor. A computation executed on P processors is time-efficient if the time is O(T 1 =P + T1 ), that is, it achieves linear speedup when P = O(T 1 =T1 ), and it is space-efficient if it uses O(S 1 P ) total space, that is, the space per processor is within a constant factor of that required for a 1-processor execution. The first result derived from this model shows that there exist multithreaded computations such that no execution schedule can simultan...

Many high-level parallel programming languages allow for fine-grained parallelism. As in the popular work-time framework for parallel algorithm design, programs written in such languages can express the full parallelism in the program without specifying the mapping of program tasks to processors. A common concern in executing such programs is to schedule tasks to processors dynamically so as to minimize not only the execution time, but also the amount of space (memory) needed. Without careful scheduling, the parallel execution on p processors can use a factor of p or larger more space than a sequential implementation of the same program. This paper first identifies a class of parallel schedules that are provably efficient in both time and space. For any

Recent work on scheduling algorithms has resulted in provable bounds on the space taken by parallel computations in relation to the space taken by sequential computations. The results for online versions of these algorithms, however, have been limited to computations in which threads can only synchronize with ancestor or sibling threads. Such computations do not include languages with futures or user-specified synchronization constraints. Here we extend the results to languages with synchronization variables. Such languages include languages with futures, such as Multilisp and Cool, as well as other languages such asid. The main result is an online scheduling algorithm which, given a computation with w work (total operations), synchronizations, d depth (critical path) and s1 sequential space, will run in O(w=p + log(pd)=p + d log(pd)) time and s1 + O(pd log(pd)) space, on a p-processor crcw pram with a fetch-and-add primitive. This includes all time and space costs for both the computation and the scheduler. The scheduler is non-preemptive in the sense that it will only move a thread if the thread suspends on a synchronization, forks a new thread, or exceeds a threshold when allocating space. For the special case where the computation is a planar graph with left-to-right synchronization edges, the scheduling algorithm can be implemented in O(w=p+d log p) time and s1 + O(pd log p) space. These are the first nontrivial space bounds described for such languages.

This article presents an on-line scheduling algorithm that is provably space e#cient and time e#cient for nested-parallel languages. For a computation with depth D and serial space requirement S1 , the algorithm generates a schedule that requires at most S1 +O(K D p)space (including scheduler space) on p processors. Here, K is a user-adjustable runtime parameter specifying the net amount of memory that a thread may allocate before it is preempted by the scheduler. Adjusting the value of K provides a trade-o# between the running time and the memory requirement of a parallel computation. To allow the scheduler to scale with the number of processors, we also parallelize the scheduler and analyze the space and time bounds of the computation to include scheduling costs. In addition to showing that the scheduling algorithm is space and time e#cient in theory, we demonstrate that it is e#ective in practice. We have implemented a runtime system that uses our algorithm to schedule lightweight parallel threads. The results of executing parallel programs on this system show that our scheduling algorithm significantly reduces memory usage compared to previous techniques, without compromising performance

The running time and memory requirement of a parallel program with dynamic, lightweight threads depends heavily on the underlying thread scheduler. In this paper, we present a simple, asynchronous, space-efficient scheduling algorithm for shared memory machines that combines the low scheduling overheads and good locality of work stealing with the low space requirements of depth-first schedulers. For a nested-parallel program with depth D and serial space requirement S 1 , we show that the expected space requirement is S 1 +O(K \Delta p \Delta D) on p processors. Here, K is a user-adjustable runtime parameter, which provides a tradeoff between running time and space requirement. Our algorithm achieves good locality and low scheduling overheads by automatically increasing the granularity of the work scheduled on each processor. We have implemented the new scheduling algorithm in the context of a native, user-level implementation of Posix standard threads or Pthreads, and evaluated its p...

Many of today's high level parallel languages support dynamic, fine-grained parallelism. These languages allow the user to expose all the parallelism in the program, which is typically of a much higher degree than the number of processors. Hence an efficient scheduling algorithm is required to assign computations to processors at runtime. Besides having low overheads and good load balancing, it is important for the scheduling algorithm to minimize the space usage of the parallel program. This paper presents a scheduling algorithm that is provably space-efficient and time-efficient for nested parallel languages. In addition to proving the space and time bounds of the parallel schedule generated by the algorithm, we demonstrate that it is efficient in practice. We have implemented a runtime system that uses our algorithm to schedule parallel threads. The results of executing parallel programs on this system show that our scheduling algorithm significantly reduces memory usage compared to...

Multithreading has become a dominant paradigm in general purpose MIMD parallel computation. To execute a multithreaded computation on a parallel computer, a scheduler must order and allocate threads to run on the individual processors. The scheduling algorithm dramatically affects both the speedup attained and the space used when executing the computation. We consider the problem of scheduling multithreaded computations to achieve linear speedup without using significantly more space-per-processor than required for a single-processor execution. We show that for general multithreaded computations, no scheduling algorithm can simultaneously make efficient use of space and time. In particular, we show that there exist multithreaded computations such that any execution schedule X that achieves P-processor execution time T P (X ) T 1 =ae, where T 1 is the minimum possible serial execution time, must use space at least S P (X ) 1 4 (ae \Gamma 1) p T 1 + S 1 , where S 1 is the space use...

OF DISSERTATION CODE GENERATIONS, EVALUATIONS, AND OPTIMIZATIONS IN MULTITHREADED EXECUTIONS Efficient large-scale parallel processing can result only from proper handling of latency. Latency arises either from remote memory accesses or synchronizations. Multithreading is an execution model that can effectively deal with latency by switching among a set of ready threads. This model has been proposed in a variety of forms: a unit of storage can be based on either a collection of threads or a single thread, threads can be either blocking or non-blocking, and synchronization can be either implicit or explicit. This dissertation describes research in the evaluation and optimization of various issues in multithreading. Issues of particular interest are the development of a multithreaded execution model to be used as a test-bed and a hybrid code generation scheme where threads are generated in a top-down manner and then optimized in a bottom-up fashion. Various forms of locality are also ide...