Performing work in broadcast networks

Abstract

We consider the problem of how to schedule t similar and independent tasks to be performed in a synchronous distributed system of p stations communicating via multiple-access channels. Stations are prone to crashes whose patterns of occurrence are specified by adversarial models. Work, defined as the number of the available processor steps, is the complexity measure. We consider only reliable algorithms that perform all the tasks as long as at least one station remains operational. It is shown that every reliable algorithm has to perform work (t + p √ t) even when no failures occur. An optimal deterministic algorithm for the channel with collision detection is developed, which performs work O(t + p √ t). Another algorithm, for the channel without collision detection, performs work O(t + p √ t + p min{ f, t}), where f < p is the number of failures. This algorithm is proved to be optimal, provided that the adversary is restricted in failing no more than f stations. Finally, we consider the question if randomization helps against weaker adversaries for the channel without collision detection. A randomized algorithm is developed which performs the expected minimum amount O(t + p √ t) of work, provided that the adversary may fail a constant fraction of stations and it has to select failure-prone stations prior to the start of an execution of the algorithm.

A robust randomized algorithm to perform independent tasks

“…Fernández, Georgiou, Russell, and Shvartsman [8] considered Do-All in the model of Byzantine failures. Chlebus, Kowalski and Lingas [4] and Clementi, Monti and Silvestri [5] investigated the Do-All problem in distributed systems in which communication is by way of a multiple-access channel. Paper [4] considered the impact of collision detection and randomization on the work complexity of protocols.…”

“…Chlebus, Kowalski and Lingas [4] and Clementi, Monti and Silvestri [5] investigated the Do-All problem in distributed systems in which communication is by way of a multiple-access channel. Paper [4] considered the impact of collision detection and randomization on the work complexity of protocols. The solutions to Do-All in [4] were required to be correct against the unbounded adversary.…”

“…Paper [4] considered the impact of collision detection and randomization on the work complexity of protocols. The solutions to Do-All in [4] were required to be correct against the unbounded adversary. Paper [5] studied F -reliable protocols that are correct if the number of crashes is at most F , for a parameter F < p. They obtained tight bounds on the time and work of F -reliable deterministic protocols.…”

Fault-Tolerant Parallel Scheduling of Arbitrary Length Jobs on a Shared Channel

“…We examine the problem of performing n jobs by m machines reliably on a multipleaccessed shared channel (MAC). This problem in such model, originated by Chlebus, Kowalski and Lingas [6], has already been studied for unit length jobs, whereas this paper extends it by considering jobs with arbitrary lengths, studying the impact of features including preemption, randomization, and severity of failures on the work performance.…”

Broadcasting Spanning Forests on a Multiple-Access Channel

“…Martel and Vayda [29,30] studied the problem of finding the maximum value among those stored at a subset of stations. Chlebus et al [7] and Clementi et al [8] considered the problem of performing a set of independent unit tasks, when the stations may fail by crashing. This problem is called Do-All, it was first studied in a message-passing model by Dwork et al [10].…”