We study some classical problems in scheduling. In the rst problem a sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time(pj) is known. We have to assign the job to one of the machines immediately, without knowledge of the jobs that arrive later. Jobs cannot be preempted. The goal is to minimize the makespan, the time when the last job is completed. The second problem deals with scheduling jobs on a single machine/processor. With each job we have an associated weight(wj), release time(rj) and processing time(pj). Now the objective is to minimize the weighted sum of completion times,Pnj=0wjCj . The constraints are that a job can only be scheduled after its release time, and preemption is not allowed. In the third problem again there are m machines. Each job has to visit the machines in the same xed order. The processing time pij of job j on machine i is known. We want a schedule which minimizes the makespan. A job can only be processed on a single machine at a time. Chapter

OR Scheduling Algorithms

We have seen a variety of on-line scheduling problems. Many of them are understood satisfactorily, but there are also many interesting open problems. Studied scheduling problems differ not only in the setting and numerical results, but also in the techniques used. In this way on-line scheduling illustrates many general aspects of competitive analysis.

On-line Scheduling

We present a new on-line algorithm, MR, for non-preemptive scheduling of jobs with known processing times on m identical machines which beats the best previous algorithm for m⩾64. For m∞ its competitive ratio approaches 1+\sqrt{(1+1{\rm n} 2)/2}<1.9201. Copyright 2000 © John Wiley & Sons, Ltd.

On‐line scheduling revisited

We survey on-line load balancing on various models.

On-line Load Balancing

On-line scheduling --- a survey

Logo detection in document images

The problem of scheduling independent jobs on m parallel machines in an online fashion was introduced by Graham in 1966. While the deterministic case of this problem has been studied extensively, little work has been done on the randomized case. For m = 2 an algorithm achieving a competitive ratio of 4/3 was found by Bartal, Fiat, Karloff and Vohra. These same authors show a matching lower bound. Chen, van Vliet and Woeginger, and independently Sgall, have shown a lower bound which converges to \(\frac{e}{{e - 1}}\)as m goes to infinity. Prior to this work, no randomized algorithm for m > 2 was known. A randomized algorithm for m ≥ 3 is presented. It achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295 and 1.81681, for m = 3,..., 7 respectively. These competitive ratios are less than the best deterministic lower bound for m = 3, 4, 5 and less than the competitive ratio of the best deterministic algorithm for m < 7.

Randomized Algorithms for that Ancient Scheduling Problem

This paper is concerned with online caching algorithms for the (n, k)-companion cache, defined by Brehob et. al. [3]. In this model the cache is composed of two components: a k-way set-associative cache and a companion fully-associative cache of size n. We show that the deterministic competitive ratio for this problem is (n+1)(k+1)-1, and the randomized competitive ratio is O(log n log k) and Ω(log n + log k).

Online companion caching

This paper is concerned with online cachingalg orithms for the (n, k)-companion cache, defined by Brehob et. al. [3]. In this model the cache is composed of two components: a k-way set-associative cache and a companion fully-associative cache of size n. We show that the deterministic competitive ratio for this problem is (n+1)(k+1) - 1, and the randomized competitive ratio is O(log n log k) and ?(log n + log k).

Steven S. Seiden

Papers

Logo detection in document images

Randomized Algorithms for that Ancient Scheduling Problem

Online companion caching

Online Companion Caching