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33
Online Load Balancing
 Theoretical Computer Science
, 1992
"... . We survey online load balancing on various models. 1 Introduction General: The machine load balancing problem is defined as follows: There are n parallel machines and a number of independent tasks (jobs); the tasks arrive at arbitrary times, where each task has an associated load vector and dur ..."
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Cited by 100 (15 self)
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. We survey online load balancing on various models. 1 Introduction General: The machine load balancing problem is defined as follows: There are n parallel machines and a number of independent tasks (jobs); the tasks arrive at arbitrary times, where each task has an associated load vector and duration. A task has to be assigned immediately to exactly one of the machines, thereby increasing the load on this machine by the amount specified by the corresponding coordinate of the load vector for the duration of the task. All tasks must be assigned, i.e., no admission control is allowed. The goal is usually to minimize the maximumload, but we also consider other goal functions. We mainly consider nonpreemptive load balancing, but in some cases we may allow preemption i.e., reassignments of tasks. All the decisions are made by a centralized controller. The online load balancing problem naturally arises in many applications involving allocation of resources. As a simple concrete example,...
New Algorithms for an Ancient Scheduling Problem
, 1992
"... We consider the online version of the original mmachine scheduling problem: given m machines and n positive real jobs, schedule the n jobs on the m machines so as to minimize the makespan, the completion time of the last job. In the online version, as soon as job j arrives, it must be assigned im ..."
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Cited by 92 (4 self)
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We consider the online version of the original mmachine scheduling problem: given m machines and n positive real jobs, schedule the n jobs on the m machines so as to minimize the makespan, the completion time of the last job. In the online version, as soon as job j arrives, it must be assigned immediately to one of the m machines. We present two main results. The first is a (2  ffl)competitive deterministic algorithm for all m. The competitive ratio of all previous algorithms approaches 2 as m !1. Indeed, the problem of improving the competitive ratio for large m had been open since 1966, when the first algorithm for this problem appeared. The second result is an optimal randomized algorithm for the case m = 2. To the best of our knowledge, our 4/3competitive algorithm is the first specifically randomized algorithm for the original, mmachine, online scheduling problem.
Better Bounds For Online Scheduling
 SIAM JOURNAL ON COMPUTING
, 1997
"... We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986c ..."
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Cited by 75 (3 self)
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We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986competitive. Karger, Phillips and Torng [11] generalized the algorithm and proved an upper bound of 1.945. The best lower bound currently known on the competitive ratio that can be achieved by deterministic online algorithms it equal to 1.837. In this paper we present an improved deterministic online scheduling algorithm that is 1.923competitive, for all m 2. The algorithm is based on a new scheduling strategy, i.e., it is not a generalization of the approach by Bartal et al. Also, the algorithm has a simple structure. Furthermore, we develop a better lower bound. We prove that, for general m, no deterministic online scheduling algorithm can be better than 1.852competitive.
The kserver problem
 Computer Science Review
"... The kserver problem is perhaps the most influential online problem: natural, crisp, with a surprising technical depth that manifests the richness of competitive analysis. The kserver conjecture, which was posed more that two decades ago when the problem was first studied within the competitive ana ..."
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Cited by 66 (5 self)
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The kserver problem is perhaps the most influential online problem: natural, crisp, with a surprising technical depth that manifests the richness of competitive analysis. The kserver conjecture, which was posed more that two decades ago when the problem was first studied within the competitive analysis framework, is still open and has been a major driving force for the development of the area online algorithms. This article surveys some major results for the kserver. 1
A Better Algorithm For an Ancient Scheduling Problem
 Journal of Algorithms
, 1996
"... One of the oldest and simplest variants of multiprocessor scheduling is the online scheduling problem studied by Graham in 1966. In this problem, the jobs arrive online and must be scheduled nonpreemptively on m identical machines so as to minimize the makespan. The size of a job is known on arri ..."
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Cited by 60 (2 self)
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One of the oldest and simplest variants of multiprocessor scheduling is the online scheduling problem studied by Graham in 1966. In this problem, the jobs arrive online and must be scheduled nonpreemptively on m identical machines so as to minimize the makespan. The size of a job is known on arrival. Graham proved that the List Processing Algorithm which assigns each job to the currently least loaded machine has competitive ratio (2 \Gamma 1=m). Recently algorithms with smaller competitive ratios than List Processing have been discovered, culminating in Bartal, Fiat, Karloff, and Vohra's construction of an algorithm with competitive ratio bounded away from 2. Their algorithm has a competitive ratio of at most (2 \Gamma 1=70) 1:986 for all m; hence for m ? 70, their algorithm is provably better than List Processing. We present a more natural algorithm that outperforms List Processing for any m 6 and has a competitive ratio of at most 1:945 for all m, which is significantly closer ...
Multiprocessor Scheduling with Rejection
, 1996
"... We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by m identical parallel machines and a set of n jobs, each job characterized by a processing time and a penalty. In the online version t ..."
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Cited by 38 (3 self)
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We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by m identical parallel machines and a set of n jobs, each job characterized by a processing time and a penalty. In the online version the jobs arrive one by one and we have to schedule or reject a job before we have any information about future jobs. The objective is to minimize the makespan of the schedule for accepted jobs plus the sum of the penalties of rejected jobs. The main result is a 1 + OE 2:618 competitive algorithm for the online version of the problem, where OE is the golden ratio. A matching lower bound shows that this is the best possible algorithm working for all m. For fixed m we give improved bounds, in particular for m = 2 we give an optimal OE 1:618 competitive algorithm. For the offline problem we present a fully polynomial approximation scheme for fixed m and a polynomial approximation sche...
A Lower Bound for Randomized OnLine Multiprocessor Scheduling
, 1997
"... We significantly improve the previous lower bounds on the performance of randomized algorithms for online scheduling jobs on m identical machines. We also show that a natural idea for constructing an algorithm with matching performance does not work. Keywords combinatorial problems, online algorit ..."
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Cited by 37 (3 self)
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We significantly improve the previous lower bounds on the performance of randomized algorithms for online scheduling jobs on m identical machines. We also show that a natural idea for constructing an algorithm with matching performance does not work. Keywords combinatorial problems, online algorithms, randomization, scheduling, worst case bounds. 1 Introduction We study the model for scheduling introduced [7] and studied recently in [6, 1, 8]. This model is essentially a modified version of the game of Tetris. We have some fixed number of columns. Rectangles arrive one by one, each of them is one column wide and extends over one or more rows. We have to put each rectangle in one of the columns. The goal is to minimize the total number of rows that are at least partially used by the rectangles. In this scenario the columns represent the machines, rows represent the time steps and the rectangles represent the jobs with a running time corresponding to the height of a rectangle. More p...
OnLine Scheduling  A Survey
, 1997
"... Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequ ..."
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Cited by 36 (0 self)
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Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequence of jobs that have to be processed on the machines available to us. In the most basic problem, each job is characterized by its running time and has to be scheduled for that time on one of the machines. In other variants there may be additional restrictions or relaxations specifying which schedules are allowed. We want to schedule the jobs as efficiently as possible, which most often means that the total length of the schedule (the makespan) should be as small as possible, but other objective functions are also considered. The notion of an online algorithm is intended to formalize the realistic scenario, where the algorithm does not have the access to the whole inp...
Online scheduling
 Online Algorithms, Lecture Notes in Computer Science 1442
, 1998
"... Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequ ..."
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Cited by 31 (2 self)
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Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequence of jobs
Online Scheduling Revisited
, 2000
"... We present a new online algorithm, MR, for nonpreemptive scheduling of jobs with known processing times on m identical machines which beats the best previous algorithm for m 64. For m ! 1 its competitive ratio approaches 1 + q 1+ln2 2 ! 1:9201. ..."
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Cited by 30 (0 self)
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We present a new online algorithm, MR, for nonpreemptive scheduling of jobs with known processing times on m identical machines which beats the best previous algorithm for m 64. For m ! 1 its competitive ratio approaches 1 + q 1+ln2 2 ! 1:9201.