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100
NonClairvoyant Scheduling
, 1993
"... Virtually all research in scheduling theory has been concerned with clairvoyant scheduling where it is assumed that the characteristics of a job (in particular, its execution time, release time and dependence on other jobs) are known a priori. This assumption is invalid for scheduling problems t ..."
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Cited by 94 (5 self)
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Virtually all research in scheduling theory has been concerned with clairvoyant scheduling where it is assumed that the characteristics of a job (in particular, its execution time, release time and dependence on other jobs) are known a priori. This assumption is invalid for scheduling problems that arise in timesharing operating systems where the scheduler must provide fast turnaround for processes being generated by the users without any knowledge of the future behavior of these processes. We study preemptive, nonclairvoyant scheduling schemes where the scheduler has no knowledge of the jobs' characteristics. We develop a model for evaluating scheduling strategies for single and multiprocessor systems. This model compares the nonclairvoyant scheduler against the optimal clairvoyant scheduler, and it takes into account various issues such as release times, execution time, preemption cost, and the interdependence between jobs. Within this model we study some standard sc...
OnLine Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling
, 1993
"... In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and descr ..."
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Cited by 89 (4 self)
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In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and describe an algorithm that achieves an O(log n) competitive ratio with respect to maximum congestion, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, i.e. for any online algorithm there exists a scenario in which O(log n) increase in bandwidth is necessary. We view virtual circuit routing as a generalization of an online load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases this machine’s load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrelated case (with n machines), we describe a new method that yields O(log n)competitive
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 86 (5 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.
Data Partitioning and Load Balancing in Parallel Disk Systems
, 1994
"... Parallel disk systems provide opportunities for exploiting I/O parallelism in two possible ways, namely via interrequest and intrarequest parallelism. In this paper we discuss the main issues in performance tuning of such systems, namely striping and load balancing, and show their relationship to ..."
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Cited by 81 (8 self)
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Parallel disk systems provide opportunities for exploiting I/O parallelism in two possible ways, namely via interrequest and intrarequest parallelism. In this paper we discuss the main issues in performance tuning of such systems, namely striping and load balancing, and show their relationship to response time and throughput. We outline the main components of an intelligent file system that optimizes striping by taking into account the requirements of the applications, and performs load balancing by judicious file allocation and dynamic redistributions of the data when access patterns change. Our system uses simple but effective heuristics that incur only little overhead. We present performance experiments based on synthetic workloads and reallife traces.
An opportunity cost approach for job assignment in a scalable computing cluster
 IEEE Transactions on Parallel and Distributed Systems
, 2000
"... A new method is presented for job assignment to and reassignment between machines in a computing cluster. Our method is based on a theoretical framework that has been experimentally tested and shown to be useful in practice. This “opportunity cost ” method converts the usage of several heterogeneous ..."
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Cited by 67 (2 self)
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A new method is presented for job assignment to and reassignment between machines in a computing cluster. Our method is based on a theoretical framework that has been experimentally tested and shown to be useful in practice. This “opportunity cost ” method converts the usage of several heterogeneous resources in a machine to a single homogeneous “cost”. Assignment and reassignment is then performed based on that cost. This is in contrast to previous methods for job assignment and reassignment, which treat each resource as an independent entity with its own constraints. These previous methods were intrinsically ad hoc, as there was no clean way to balance one resource against another. 1.
Competitive Routing of Virtual Circuits with Unknown Duration
 In Proc. 5th ACMSIAM Symposium on Discrete Algorithms
, 1994
"... In this paper we present a strategy to route unknown duration virtual circuits in a highspeed communication network. Previous work on virtual circuit routing concentrated on the case where the call duration is known in advance. We show that by allowing O(log n) reroutes per call, we can achieve O(lo ..."
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Cited by 66 (15 self)
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In this paper we present a strategy to route unknown duration virtual circuits in a highspeed communication network. Previous work on virtual circuit routing concentrated on the case where the call duration is known in advance. We show that by allowing O(log n) reroutes per call, we can achieve O(log n) competitive ratio with respect to the maximum load (congestion) for the unknown duration case, were n is the number of nodes in the network. This is in contrast to the ( 4p n)lower bound on the competitive ratio for this case if no rerouting is allowed [3]. Our routing algorithm can be also applied in the context of machine load balancing of tasks with unknown duration. We present an algorithm that makes O(log n) reassignments per task and achieves O(log n) competitive ratio with respect to the load, where n is the number of parallel machines. For a special case of unit load tasks we design a constant competitive algorithm. The previously known algorithms that achieve up to polylogarithmic competitive ratio for load balancing of tasks with unknown duration dealt only with special cases of related machines case and unitload tasks with restricted assignment[4,11].
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 66 (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 ...
Allocating Bandwidth for Bursty Connections
 SIAM J. Comput
, 1997
"... Abstract. In this paper, we undertake the first study of statistical multiplexing from the perspective of approximation algorithms. The basic issue underlying statistical multiplexing is the following: in highspeed networks, individual connections (i.e., communication sessions) are very bursty, wit ..."
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Cited by 66 (0 self)
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Abstract. In this paper, we undertake the first study of statistical multiplexing from the perspective of approximation algorithms. The basic issue underlying statistical multiplexing is the following: in highspeed networks, individual connections (i.e., communication sessions) are very bursty, with transmission rates that vary greatly over time. As such, the problem of packing multiple connections together on a link becomes more subtle than in the case when each connection is assumed to have a fixed demand. We consider one of the most commonly studied models in this domain: that of two communicating nodes connected by a set of parallel edges, where the rate of each connection between them is a random variable. We consider three related problems: (1) stochastic load balancing, (2) stochastic binpacking, and (3) stochastic knapsack. In the first problem the number of links is given and we want to minimize the expected value of the maximum load. In the other two problems the link capacity and an allowed overflow probability p are given, and the objective is to assign connections to links, so that the probability that the load of a link exceeds the link capacity is at most p. In binpacking we need to assign each connection to a link using as few links as possible. In the knapsack problem each connection has a value, and we have only one link. The problem is to accept as many
Online Load Balancing of Temporary Tasks
, 1993
"... This paper considers the nonpreemptive online load balancing problem where tasks have limited duration in time. Upon arrival, each task has to be immediately assigned to one of the machines, increasing the load on this machine for the duration of the task by an amount that depends on both the m ..."
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Cited by 58 (11 self)
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This paper considers the nonpreemptive online load balancing problem where tasks have limited duration in time. Upon arrival, each task has to be immediately assigned to one of the machines, increasing the load on this machine for the duration of the task by an amount that depends on both the machine and the task. The goal is to minimize the maximum load. Azar, Broder and Karlin studied the unknown duration case where the duration of a task is not known upon its arrival [4]. They focused on the special case in which for each task there is a subset of machines capable of executing it, and the increase in load due to assigning the task to one of these machines depends only on the task and not on the machine. For this case, they showed an O(n 2=3 )competitive algorithm, and an \Omega\Gamma p n) lower bound on the competitive ratio, where n is the number of the machines. This paper closes the gap by giving an O( p n)competitive algorithm. In addition, trying to overco...
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 48 (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...