this paper we present a rather straightforward algorithm to solve the Write-All problem on an asynchronous PRAM, i.e. a machine on which the processes can be stopped and restarted at will. This means that it is also suitable for all other fault models as mentioned in Kanellakis and Shvartsman, page 13 [9]. Using dierent terminology we can say that our algorithm is wait-free, which means that each non-faulty process will be able to nish the whole task, within a predetermined amount of steps, independent of the actions (or failures) of other processes.

We consider the problem of performing t tasks in a distributed system of p faultprone processors. This problem, called do-all herein, was introduced by Dwork, Halpern and Waarts. Our work deals with a synchronous message-passing distributed system with processor stop-failures and restarts. We present two new algorithms based on a new aggressive coordination paradigm by which multiple coordinators may be active as the result of failures. The first algorithm is tolerant of f < p stop-failures and it does not allow restarts. It has available processor steps (work) complexity S = O((t + p log p= log log p) log f) and message complexity M = O(t + p log p= log log p + fp). Unlike prior solutions, our algorithm uses redundant broadcasts when encountering failures and, for p = t and large f , it achieves better work complexity. This algorithm is used as the basis for another algorithm that tolerates stop-failures and restarts. This new algorithm is the first solution for the do-all problem that efficiently deals with processor restarts. Its available processor steps complexity is S = O((t + p log p + f) minflog p; log fg), and its message complexity is M = O(t+p log p+fp), where f is the total number of failures.

We study the problem of executing parallel programs, in particular Cilk programs, on a collection of processors of di erent speeds. We consider a model in which each processor maintains an estimate of its own speed, where communication between processors has a cost, and where all scheduling must be online. This problem has been considered previously in the fields of asynchronous parallel computing and scheduling theory. Our model is a bridge between the assumptions in these fields. We provide a new more accurate analysis of an old scheduling algorithm called the maximum utilization scheduler. Based on this analysis, we generalize this scheduling policy and define the high utilization scheduler. We next focus on the Cilk platform and introduce a new algorithm for scheduling Cilk multithreaded parallel programs on heterogeneous processors. This scheduler is inspired by the high utilization scheduler and is modified to fit in a Cilk context. A crucial aspect of our algorithm is that it keeps the original spirit of the Cilk scheduler. In fact, when our new algorithm runs on homogeneous processors, it exactly mimics the dynamics of the original Cilk scheduler.

Do-All is the problem of performing N tasks in a distributed system of P failure-prone processors [9]. Many distributed and parallel algorithms have been developed for this basic problem and several algorithm simulations have been developed by iterating Do-All algorithms. The eciency of the solutions for Do-All is measured in terms of work complexity where all processing steps taken by the processors are counted. Work is ideally expressed as a function of N , P , and f , the number of processor crashes. However the known lower bounds and the upper bounds for extant algorithms do not adequately show how work depends on f . We present the rst non-trivial lower bounds for Do-All that capture the dependence of work on N , P and f . For the model of computation where processors are able to make perfect load-balancing decisions locally, we also present matching upper bounds. Thus we give the rst complete analysis of DoAll for this model. We dene the r-iterative Do-All problem that abstracts the repeated use of Do-All such as found in algorithm simulations. Our f-sensitive analysis enables us to derive a tight bound for r-iterative Do-All work (that is stronger than the r-fold work complexity of a single Do-All). Our approach that models perfect load-balancing allows for the analysis of specic algorithms to be divided into two parts: (i) the analysis of the cost of tolerating failures while performing work, and (ii) the analysis of the cost of implementing load-balancing. We demonstrate the utility and generality of this approach by improving the analysis of two known ecient algorithms. We give an improved analysis of an ecient message-passing algorithm (algorithm AN [5]). We also derive a new and complete analysis of the best known Do-All algorithm for...

The problem of performing t tasks in a distributed system on p failure-prone processors is one of the fundamental problems in distributed computing. If the tasks are similar and independent and the processors communicate by sending messages then the problem is called Do-All . In our work the communication is over a multiple-access channel, and the attached stations may fail by crashing. The measure of performance is work, defined as the number of the available processor steps. Algorithms are required to be reliable in that they perform all the tasks as long as at least one station remains operational. We show that each reliable algorithm always needs to perform at least the minimum amount t + p p t) of work. We develop an optimal deterministic algorithm for the channel with collision detection performing only the minimum work (t + p p t). Another algorithm is given for the channel without collision detection, it performs work O(t+p p t+p minff; tg), where f < p is the number of failures. It is proved to be optimal if the number of faults is the only restriction on the adversary. Finally we consider the question if randomization helps for the channel without collision detection against weaker adversaries. We develop a randomized algorithm which needs to perform only the expected minimum work if the adversary may fail a constant fraction of stations, but it has to select the failure-prone stations prior to the start of an algorithm.

We study the problem of executing parallel programs, in particular Cilk programs, on a collection of processors of different speeds. We consider a model in which each processor maintains an estimate of its own speed, where communication between processors has a cost, and where all scheduling must be online. This problem has been considered previously in the fields of asynchronous parallel computing and scheduling theory. Our model is a bridge between the assumptions in these fields. We provide a new more accurate analysis of an old scheduling algorithm called the maximum utilization scheduler. Based on this analysis, we generalize this scheduling policy and de ne the high utilization scheduler. We next focus on the Cilk platform and introduce a new algorithm for scheduling Cilk multithreaded parallel programs on heterogeneous processors. This scheduler is inspired by the high utilization scheduler and is modified to fit in a Cilk context. A crucial aspect of our algorithm is that it kee...

This paper shows how to create near-optimal instances of the Certified Write-All algorithm called AWT that was introduced by Anderson and Woll [2]. This algorithm is the best known deterministic algorithm that can be used to simulate n synchronous parallel processors on n asynchronous processors. In this algorithm n processors update n memory cells and then signal the completion of the updates. The algorithm is instantiated with q permutations, where q can be chosen from a wide range of values. When implementing a simulation on a specific parallel system with n processors, one would like to use an instance of the algorithm with the best possible value of q, in order to maximize the efficiency of the simulation. This paper shows that the choice of q is critical for obtaining an instance of the AWT algorithm with near-optimal work. For any > 0, and any large enough n, work of any instance of the algorithm must be at least n . Under certain conditions, however, that q is about e and for infinitely many large enough n, this lower bound can be nearly attained by instances of the algorithm with work at most n . The paper also shows a penalty for not selecting q well. When q is significantly away from e , then work of any instance of the algorithm with this displaced q must be considerably higher than otherwise.

.<F4.039e+05> In this paper, we prove new upper bounds on the complexity of the certified write-all problem with respect to an adaptive adversary. Our strongest result is that for any<F3.785e+05> # ><F4.039e+05> 0, there exists an<F3.785e+05><F4.039e+05><F3.785e+05> O(p<F3.437e+05><F3.179e+05> 1+#<F4.039e+05> ) work algorithm for the<F3.785e+05><F4.039e+05> p-processor<F3.785e+05><F4.039e+05> p-memory cell write-all. We also give a randomized<F3.785e+05><F4.039e+05><F3.785e+05> O(p<F3.437e+05> 2<F4.039e+05> log<F3.785e+05><F4.039e+05> p) work algorithm for a<F3.785e+05><F4.039e+05> p-processor<F3.785e+05> p<F3.437e+05> 2<F4.039e+05> -memory cell write-all.<F4.601e+05> Key words.<F4.039e+05> certified write-all problem, asynchronous computation, synchronization primitives, adversary models<F4.601e+05> AMS subject classifications.<F4.039e+05> 68Q10, 68Q22<F4.601e+05> PII.<F4.039e+05> S0097539794319126<F5.308e+05> 1. Introduction.<F4.753e+05> A fundamental problem in asynchronous c...