Time-optimal message-efficient work performance in the presence of faults

Abstract

Performing work in parallel by a multitude of processes in a distributed environment is currently a fast growing area of computer applications (due to its cost effectiveness). Adaptation of such applications to changes in system's parallelism (i.e., the availability of processes) is essential for improved performance and reliability y. In this work we consider one aspect of coping with dynamic processes failures in such a setting, namely the following scenario formulated by Dwork, Halpern and Waarts [DH W92]: a system of n synchronous processes that communicate only by sending messages to one another. These processes must perform m independent units of work. Processes may fail by crashing and wait-freeness is required, i.e. that whenever at least one process survives, all m units of work will be performed.We consider the notion of fast algorithms in this setting, yet we are not willing to trade improved time for a high cost in communication.Thus, we require message efficiency as well. We therefore put forth the notion of lexicographic eflciency, that is we consider the following two complexity measures in order: The parallel processor step (or S for short) as introduced by Kanellakis and Shvartsman [KS89] in the context of robust PRAM and the number of messages sent (denoted M).We present an algorithm which has S = O(m + (f + l)n) (where f denotes the actual number of failures) and prove that this is optimal (in absolute terms in all fault scenarios). Furthermore, the algorithm has M= O((f + l)n) and hence is the first messageeficient algorithm with optimal S. This is a step in understanding lexicographic efficiency, and towards solving the open problem in [DHW92] of simultaneously optimizing time and messages.

Performing tasks on synchronous restartable message-passing processors

“…Algorithms solving the do-all problem have been provided by Dwork, Halpern and Waarts [6], by De Prisco, Mayer and Yung [5], and by Galil, Mayer and Yung [7]. These deterministic algorithms are formulated for failure models that allow processor failures but disallow processor restarts.…”

“…This work measure accounts only for steps taken by processors while executing the tasks of the do-all problem; processor steps taken for coordination or waiting 1. Efficiency of the solutions in [5,7] and algorithms AN and AR (the solutions in [6] consider a different notion of work complexity and focus on evaluation of effort) for messages are not counted. Another measure of work, the available processor steps, defined by Kanellakis and Shvartsman [10], takes into account all steps taken by the processors, that is, both steps taken in executing the t tasks and any other steps, including idling, taken by the available processors.…”

“…However, this makes it difficult to compare relative efficiency of algorithms that exhibit varying trade-offs between the work and the communication efficiencies. De Prisco, Mayer and Yung [5] evaluate do-all algorithms using a "lexicographic" criterion: first evaluate an algorithm according to its available processor steps and then according to its message complexity. This approach assumes that optimization of the computational steps is more important than that of the message complexity.…”

Markov Renewal Methods in Restart Problems in Complex Systems

“…For these two schemes, see Kulkarni et al [14], [15]. Further models and methods of failure recovery are in Chlebus et al [9] for restartable processors and in De Prisco et al [10] (stage checkpointing)…”

Explicit Combinatorial Structures for Cooperative Distributed Algorithms

“…Kowalski and Shvartsman in [11] considered the asynchronous Do-All problem ( [6,5,7]): p message-passing asynchronous processors must perform t tasks, subject to the d-adversary that delays messages by up to d time units (d is unknown to the processors). They present delaysensitive upper and lower bounds on work and message complexity for the Do-All problem.…”