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148
How bad is selfish routing?
 JOURNAL OF THE ACM
, 2002
"... We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route t ..."
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Cited by 506 (27 self)
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We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times—the total latency—is minimized. In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimumlatency path available to it, given the network congestion caused by the other users. In general such a “selfishly motivated ” assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance. In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total
Optimal TimeCritical Scheduling Via Resource Augmentation
, 1997
"... We 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 worstcase analysis, no good online a ..."
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Cited by 134 (4 self)
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We 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 worstcase analysis, no good online algorithms exist for these problems, and for some variants no good offline algorithms exist unless P = NP. We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the online algorithm is allowed more resources than the optimal offline algorithm to which it is compared. Using this approach, we establish that several wellknown online algorithms, that have poor performance from an absolute worstcase perspective, are optimal for the problems in question when allowed moderately more resources. For the optimization of average flow time, these are the first results of any sort, for any NPhard version of the problem, that indicate that...
PriorityDriven Scheduling of Periodic Task Systems on Multiprocessors
, 2001
"... The scheduling of systems of periodic tasks upon multiprocessor platforms is considered. ..."
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Cited by 91 (15 self)
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The scheduling of systems of periodic tasks upon multiprocessor platforms is considered.
Scheduling in the Dark
, 1999
"... We considered nonclairvoyant multiprocessor scheduling of jobs with arbitrary arrival times and changing execution characteristics. The problem has been studied extensively when either the jobs all arrive at time zero, or when all the jobs are fully parallelizable, or when the scheduler has conside ..."
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Cited by 72 (15 self)
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We considered nonclairvoyant multiprocessor scheduling of jobs with arbitrary arrival times and changing execution characteristics. The problem has been studied extensively when either the jobs all arrive at time zero, or when all the jobs are fully parallelizable, or when the scheduler has considerable knowledge about the jobs. This paper considers for the first time this problem without any of these three restrictions and provides new upper and lower bound techniques applicable in this more difficult scenario. The results are of both theoretical and practical interest. In our model, a job can arrive at any arbitrary time and its execution characteristics can change through the life of the job from being anywhere from fully parallelizable to completely sequential. We assume that the scheduler has no knowledge about the jobs except for knowing when a job arrives and knowing when it completes. (This is why we say that the scheduler is completely in the dark.) Given all this, we prove t...
Hedging uncertainty: Approximation algorithms for stochastic optimization problems
 In Proceedings of the 10th International Conference on Integer Programming and Combinatorial Optimization
, 2004
"... We initiate the design of approximation algorithms for stochastic combinatorial optimization problems; we formulate the problems in the framework of twostage stochastic optimization, and provide nearly tight approximation algorithms. Our problems range from the simple (shortest path, vertex cover, ..."
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Cited by 66 (10 self)
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We initiate the design of approximation algorithms for stochastic combinatorial optimization problems; we formulate the problems in the framework of twostage stochastic optimization, and provide nearly tight approximation algorithms. Our problems range from the simple (shortest path, vertex cover, bin packing) to complex (facility location, set cover), and contain representatives with different approximation ratios. The approximation ratio of the stochastic variant of a typical problem is of the same order of magnitude as its deterministic counterpart. Furthermore, common techniques for designing approximation algorithms such as LP rounding, the primaldual method, and the greedy algorithm, can be carefully adapted to obtain these results. 1
Algorithmic problems in power management
 SIGACT News
, 2005
"... We survey recent research that has appeared in the theoretical computer science literature on algorithmic ..."
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Cited by 55 (3 self)
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We survey recent research that has appeared in the theoretical computer science literature on algorithmic
Online Weighted Flow Time and Deadline Scheduling
 In RANDOMAPPROX
, 2001
"... In this paper we study some aspects of Weighted Flow Time on parallel machines. We first show that the online algorithm Highest Density First is an O(1)speed O(1)approximation algorithm for P jr i ; pmtnj P w i F i . We then consider a related Deadline Scheduling Problem that involves minimizing t ..."
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Cited by 42 (19 self)
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In this paper we study some aspects of Weighted Flow Time on parallel machines. We first show that the online algorithm Highest Density First is an O(1)speed O(1)approximation algorithm for P jr i ; pmtnj P w i F i . We then consider a related Deadline Scheduling Problem that involves minimizing the weight of the jobs unfinished by some unknown deadline D on a uniprocessor. We show that any ccompetitive online algorithm for weighted flow time must also be ccompetitive for Deadline Scheduling. We finally give an O(1)competitive algorithm for Deadline Scheduling. 1
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...
Preemptive scheduling of parallel jobs on multiprocessors
 In SODA
, 1996
"... Abstract. We study the problem of processor scheduling for n parallel jobs applying the method of competitive analysis. We prove that for jobs with a single phase of parallelism, a preemptive scheduling algorithm without information about job execution time can achieve a mean completion time within ..."
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Cited by 36 (3 self)
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Abstract. We study the problem of processor scheduling for n parallel jobs applying the method of competitive analysis. We prove that for jobs with a single phase of parallelism, a preemptive scheduling algorithm without information about job execution time can achieve a mean completion time within 2 − 2 2 times the optimum. In other words, we prove a competitive ratio of 2 − n+1 n+1. The result is extended to jobs with multiple phases of parallelism (which can be used to model jobs with sublinear speedup) and to interactive jobs (with phases during which the job has no CPU requirements) to derive solutions guaranteed to be within 4 − 4 times the optimum. In comparison n+1 with previous work, our assumption that job execution times are unknown prior to their completion is more realistic, our multiphased job model is more general, and our approximation ratio (for jobs with a single phase of parallelism) is tighter and cannot be improved. While this work presents theoretical results obtained using competitive analysis, we believe that the results provide insight into the performance of practical multiprocessor scheduling algorithms that operate in the absence of complete information.
NPHardness of Broadcast Scheduling and Inapproximability of SingleSource Unsplittable Mincost Flow
 PROCEEDINGS OF THE 13TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA’02), PP. 194–202. C ○ SIAM 2002.
, 2002
"... We consider the version of broadcast scheduling where a server can transmit one message of a given set at each timestep, answering previously made requests for that message. The goal is to minimize the average response time if the amount of requests is known in advance for each timestep and message ..."
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Cited by 35 (3 self)
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We consider the version of broadcast scheduling where a server can transmit one message of a given set at each timestep, answering previously made requests for that message. The goal is to minimize the average response time if the amount of requests is known in advance for each timestep and message. We prove that this problem is NPhard, thus answering an open question stated by Kalyanasundaram, Pruhs and Velauthapillai (Proceedings of ESA 2000, LNCS