Joel Wein

Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms

In this paper we introduce two general techniques for the design and analysis of approximation algorithms for NP-hard scheduling problems in which the objective is to minimize the weighted sum of the job completion times. For a variety of scheduling models, these techniques yield the first algorithms that are guaranteed to find schedules that have objective function value within a constant factor of the optimum. In the first approach, we use an optimal solution to a linear programming relaxation in order to guide a simple list-scheduling rule. Consequently, we also obtain results about the strength of the relaxation. Our second approach yields on-line algorithms for these problems: in this setting, we are scheduling jobs that continually arrive to be processed and, for each time t, we must construct the schedule until time t without any knowledge of the jobs that will arrive afterwards. Our on-line technique yields constant performance guarantees for a variety of scheduling environments, and in some cases essentially matches the performance of our off-line LP-based algorithms.

Optimal time-critical scheduling via resource augmentation

AbstractWe consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worst-case analysis, no good on-line algorithms exist for these problems, and for some variants no good off-line algorithms exist unless P = NP .We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the on-line algorithm is allowed more resources than the optimal off-line algorithm to which it is compared. Using this approach, we establish that several well-known on-line algorithms, that have poor performance from an absolute worst-case perspective, are optimal for the problems in question when allowed moderately more resources. For optimization of average flow time, these are the first results of any sort, for any NP -hard version of the problem, that indicate that it might be possible to design good approximation algorithms.

Scheduling Parallel Machines On-line

The problem of scheduling jobs on parallel machines is studied when (1) the existence of a job is not known until its unknown release date and (2) the processing requirement of a job is not known until the job is processed to completion. Two general algorithmic techniques are demonstrated for converting existing polynomial-time algorithms that require complete knowledge about the input data into algorithms that need less advance knowledge. Information-theoretic lower bounds on the length of on-line schedules are proven for several basic parallel machine models, and that almost all of our algorithms construct schedules with lengths that either match or come within a constant factor of the lower bound.

Minimizing average completion time in the presence of release dates

A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of schedulingn jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NP-hard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constant-factor approximation algorithms for several variants of the single and parallel machine models. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of averageweighted completion time as well.

Techniques for scheduling with rejection

We consider the general problem of scheduling a set of jobs where we may choose not to schedule certain jobs, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the sum of the weighted completion times of the jobs scheduled plus the sum of the penalties of the jobs rejected. We give several techniques for designing scheduling algorithms under this criterion. Many of these techniques show how to reduce a problem with rejection to a (potentially more complex) scheduling problem without rejection. Some of the reductions are based on general properties of certain kinds of linear-programming relaxations of optimization problems, and therefore are applicable to problems outside of scheduling; we demonstrate this by giving an approximation algorithm for a variant of the facility-location problem.

Improved Scheduling Algorithms for Minsum Criteria

We consider the problem of finding near-optimal solutions for a variety of NP-hard scheduling problems for which the objective is to minimize the total weighted completion time. Recent work has led to the development of several techniques that yield constant worst-case bounds in a number of settings. We continue this line of research by providing improved performance guarantees for several of the most basic scheduling models, and by giving the first constant performance guarantee for a number of more realistically constrained scheduling problems. For example, we give an improved performance guarantee for minimizing the total weighted completion time subject to release dates on a single machine, and subject to release dates and/or precedence constraints on identical parallel machines. We also give improved bounds on the power of preemption in scheduling jobs with release dates on parallel machines.

Load-sharing in heterogeneous systems via weighted factoring

Jeanette Schmidt~ R. N. Uma

Scheduling jobs that arrive over time

Joel Wein~ We consider the problem of scheduling a parallel loop with independent iterations on a network of heterogeneous workstations, and demonstrate the effectiveness of a variant of fa.toring, a scheduling policy originating in the context of shared address-space homogeneous multiprocessors. In the new scheme, weighted factoring, processors are dynamically assigned decreasing size chunks of iterations in proportion to their processing speeds. Through experiments on a network of SUN Spare workstations we show that weighted factoring significantly outperforms variants of a work-stea!ing load-balancing algorithm and on certain applications dramatically outperforms factoring as well. We then study weighted work assignment analytically, giving upper and lower bounds on its performance under the assumption that the processor iteration execution times can be modeled as weighted random variables. *Department of Computer Science,Polytechmc Umverslty, Brooklyn, NY, 11201. Researchsupported by ARPA/USAF under Grant no F30602-95-1-OO08and the New York State Science and Technology Foundation through Its center for Advanced Technology in Telecommunications Joel Wein wassupported in part by NSF Grant CCR-9211494, and Jeanette Schmidt m part by NSF grant CCR9305873. thummelQmono poly edu (Contact Author) *JpsC!qmcs4 poly.edu

On the Existence of Schedules that are Near-Optimal for both Makespan and Total Weighted Completion time

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Scheduling parallel machines on-line

A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NP-hard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constant-factor approximation algorithms for several variants of the single and parallel machine model. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of average weighted completion time as well.