Randomized On-line Scheduling of Parallel Jobs

doi:10.1006/jagm.1996.0041

Journal of Algorithms

Volume 21, Issue 1, July 1996, Pages 149-175

https://doi.org/10.1006/jagm.1996.0041 Get rights and content

Abstract

We study randomized on-line scheduling on mesh machines. We show that for scheduling independent jobs randomized algorithms can achieve a significantly better performance than deterministic ones; on the other hand with dependencies randomization does not help.

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Cited by (13)

Average-case performance analysis of scheduling random parallel tasks with precedence constraints on mesh connected multicomputer systems
2006, Journal of Parallel and Distributed Computing
We investigate the problem of scheduling parallel tasks with precedence constraints on mesh connected multicomputer systems. It is still an open problem on whether there exists an approximation algorithm with finite asymptotic worst-case and/or average-case performance bound for this scheduling problem. As an early attempt to solve our problem, we propose and analyze the performance of a level-by-level scheduling algorithm LL. In fact, we solve a special case of the problem when all tasks request for square submeshes and run on a square mesh system whose size is a power of 2. There are three basic techniques in algorithm LL, i.e., the level-by-level scheduling strategy for handling precedence constraints, the largest-task-first algorithm for scheduling tasks in the same level, and the two-dimensional buddy system for system partitioning and processor allocation. Algorithm LL does not have a finite worst-case performance bound; however, it has quite acceptable average-case performance. The main contribution of the paper is to show that under the assumptions that task sizes are independent and identically distributed (i.i.d.) random variables with a common probability distribution, and that task execution times are i.i.d. random variables with finite mean and variance, and that the probability distributions of task sizes and execution times are independent of each other, for wide task graphs and typical task size distributions, algorithm LL has an asymptotic average-case performance bound about two for all probability distributions of task execution times.
Maximizing job completions online
2003, Journal of Algorithms
We consider the problem of maximizing the number of jobs completed by their deadline in an online single processor system where the jobs are preemptable and have release times. So in the standard three field scheduling notation, this is the online version of the problem 1∣r_i;pmtn∣∑(1−U_i). We present a deterministic algorithm Lax, and show that for every instance $I$ , it is the case that either Lax, or the well-known deterministic algorithm SRPT (Shortest Remaining Processing Time), is constant competitive on $I$ . An immediate consequence of this result is a constant competitive randomized algorithm for this problem. It is known that no constant competitive deterministic algorithm exists for this problem.
Scheduling data transfers in a network and the set scheduling problem
2003, Journal of Algorithms
In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum.
Parallel Jobs Scheduling with a Specific Due Date: a Semi-Definite Relaxation-Based Algorithm
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Performance analysis of a scheduling algorithm for assigning squared mesh tasks in a distributed computing environment
2013, Far East Journal of Mathematical Sciences

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^*: This research was done at Carnegie-Mellon University, Pittsburgh, PA.

^†: E-mail: [email protected].

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Regular ArticleRandomized On-line Scheduling of Parallel Jobs

Abstract

Regular Article
Randomized On-line Scheduling of Parallel Jobs