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162
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 131 (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...
Flow and Stretch Metrics for Scheduling Continuous Job Streams
 In Proceedings of the 9th Annual ACMSIAM Symposium on Discrete Algorithms
, 1998
"... this paper, we isolate and study the problem of scheduling a continuous stream of requests of varying sizes. More precisely, assume a request or job j has ..."
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Cited by 126 (9 self)
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this paper, we isolate and study the problem of scheduling a continuous stream of requests of varying sizes. More precisely, assume a request or job j has
A constantfactor approximation algorithm for the multicommodity rentorbuy problem
 In Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science
, 2002
"... We present the first constantfactor approximation algorithm for network design with multiple commodities and economies of scale. We consider the rentorbuy problem, a type of multicommodity buyatbulk network design in which there are two ways to install capacity on any given edge. Capacity can b ..."
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Cited by 83 (9 self)
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We present the first constantfactor approximation algorithm for network design with multiple commodities and economies of scale. We consider the rentorbuy problem, a type of multicommodity buyatbulk network design in which there are two ways to install capacity on any given edge. Capacity can be rented, with cost incurred on a perunit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph and a set of sourcesink pairs, we seek a minimumcost way of installing sufficient capacity on edges so that a prescribed amount of flow can be sent simultaneously from each source to the corresponding sink. Recent work on buyatbulk network design has concentrated on the special case where all sinks are identical; existing constantfactor approximation algorithms for this special case make crucial use of the assumption that all commodities ship flow to the same sink vertex and do not obviously extend to the multicommodity rentorbuy problem. Prior to our work, the best heuristics for the multicommodity rentorbuy problem achieved only logarithmic performance guarantees and relied on the machinery of relaxed metrical task systems or of metric embeddings. By contrast, we solve the network design problem directly via a novel primaldual algorithm. 1
Approximation Techniques for Average Completion Time Scheduling
, 1997
"... We consider the problem of nonpreemptive scheduling to minimize average (weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led to constantfactor approximations for this problem, based on solving a preemptive or linear programming ..."
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Cited by 82 (8 self)
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We consider the problem of nonpreemptive scheduling to minimize average (weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led to constantfactor approximations for this problem, based on solving a preemptive or linear programming relaxation and then using the solution to get an ordering on the jobs. We introduce several new techniques which generalize this basic paradigm. We use these ideas to obtain improved approximation algorithms for onemachine scheduling to minimize average completion time with release dates. In the process, we obtain an optimal randomized online algorithm for the same problem that beats a lower bound for deterministic online algorithms. We consider extensions to the case of parallel machine scheduling, and for this we introduce two new ideas: first, we show that a preemptive onemachine relaxation is a powerful tool for designing parallel machine scheduling algorithms that simultaneously pro...
Approximating Total Flow Time on Parallel Machines
, 1997
"... We consider the problem of optimizing the total flow time of a stream of jobs that are released over time in a multiprocessor setting. This problem is NP hard even when we allow preemption, and have only two machines. Although the total (or average) flow time is widely accepted as a good measuremen ..."
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Cited by 68 (7 self)
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We consider the problem of optimizing the total flow time of a stream of jobs that are released over time in a multiprocessor setting. This problem is NP hard even when we allow preemption, and have only two machines. Although the total (or average) flow time is widely accepted as a good measurement of the overall quality of service, no approximation algorithms were known for this basic scheduling problem. This paper contains two main results. We first prove that when preemption is allowed, Shortest Remaining Processing Time (SRPT) is an O(log(minf n m
Improved scheduling algorithms for minsum criteria
 Automata, Languages and Programming, volume 1099 of Lecture Notes in Computer Science
, 1996
"... Abstract. We consider the problem of finding nearoptimal solutions for a variety of A/I)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 worstcase bounds in a number ..."
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Cited by 65 (18 self)
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Abstract. We consider the problem of finding nearoptimal solutions for a variety of A/I)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 worstcase 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. We give improved online algorithms for many more realistic scheduling models, including environments with parallelizable jobs, jobs contending for shared resources, tree precedenceconstrained jobs, as well as shop scheduling models. In several of these cases, we give the first constant performance guarantee achieved online. Finally, one of the consequences of our work is the surprising structural property that there are schedules that simultaneously approximate the optimal makespan and the optimal weighted completion time to within small constants. Not only do such schedules exist, but we can find approximations to them with an online algorithm. 1
Scheduling Algorithms
, 1997
"... Introduction Scheduling theory is concerned with the optimal allocation of scarce resources to activities over time. The practice of this field dates to the first time two humans contended for a shared resource and developed a plan to share it without bloodshed. The theory of the design of algorith ..."
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Cited by 64 (1 self)
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Introduction Scheduling theory is concerned with the optimal allocation of scarce resources to activities over time. The practice of this field dates to the first time two humans contended for a shared resource and developed a plan to share it without bloodshed. The theory of the design of algorithms for scheduling is younger, but still has a significant historythe earliest papers in the field were published more than forty years ago. Scheduling problems arise in a variety of settings, as is illustrated by the following examples: Example 1: Consider the central processing unit of a computer that must process a sequence of jobs that arrive over time. In what order should the jobs be processed in order to minimize, on average, the time that a job is in the system from arrival to completion? Example 2: Consider a team of five astronauts preparing for the reentry of their space shuttle into the at
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
 IN PROCEEDINGS OF THE 40TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 1999
"... We consider the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemes for several variants of this problem. Our results include PTASs for the case of identical parallel ..."
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Cited by 58 (16 self)
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We consider the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemes for several variants of this problem. Our results include PTASs for the case of identical parallel machines and a constant number of unrelated machines with and without preemption allowed. Our schemes are efficient: for all variants the running time for a (1 + ffl) approximation is of the form f(1=ffl; m)poly(n).
Scheduling to Minimize Total Weighted Completion Time: Performance Guarantees of LPBased Heuristics and Lower Bounds
"... There has been recent success in using polyhedral formulations of scheduling problems not only to obtain good lower bounds in practice but also to develop provably good approximation algorithms. Most of these formulations rely on binary decision variables that are a kind of assignment variables. We ..."
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Cited by 51 (11 self)
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There has been recent success in using polyhedral formulations of scheduling problems not only to obtain good lower bounds in practice but also to develop provably good approximation algorithms. Most of these formulations rely on binary decision variables that are a kind of assignment variables. We present quite simple polynomialtime approximation algorithms that are based on linear programming formulations with completion time variables and give the best known performance guarantees for minimizing the total weighted completion time in several scheduling environments. This amplifies the importance of (appropriate) polyhedral formulations in the design of approximation algorithms with good worstcase performance guarantees. In particular, for the problem of minimizing the total weighted completion time on a single machine subject to precedence constraints we present a polynomialtime approximation algorithm with performance ratio better than 2. This outperforms a (4 + e)approximation algorithm