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139
Scheduling to Minimize Average Completion Time: Offline and Online Algorithms
, 1996
"... Timeindexed linear programming formulations have recently received a great deal of attention for their practical effectiveness in solving a number of singlemachine scheduling problems. We show that these formulations are also an important tool in the design of approximation algorithms with good wo ..."
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Cited by 197 (27 self)
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Timeindexed linear programming formulations have recently received a great deal of attention for their practical effectiveness in solving a number of singlemachine scheduling problems. We show that these formulations are also an important tool in the design of approximation algorithms with good worstcase performance guarantees. We give simple new rounding techniques to convert an optimal fractional solution into a feasible schedule for which we can prove a constantfactor performance guarantee, thereby giving the first theoretical evidence of the strength of these relaxations. Specifically, we consider the problem of minimizing the total weighted job completion time on a single machine subject to precedence constraints, and give a polynomialtime (4 + ffl)approximation algorithm, for any ffl ? 0; the best previously known guarantee for this problem was superlogarithmic. With somewhat larger constants, we also show how to extend this result to the case with release date constraints, ...
Scheduling algorithms and operating systems support for realtime systems
 PROCEEDINGS OF THE IEEE
, 1994
"... This paper summarizes the state of the realtime field in the areas of scheduling and operating system kernels. Given the vast amount of work that has been done by both the operations research and computer science communities in the scheduling area, we discuss four paradigms underlying the schedulin ..."
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Cited by 115 (1 self)
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This paper summarizes the state of the realtime field in the areas of scheduling and operating system kernels. Given the vast amount of work that has been done by both the operations research and computer science communities in the scheduling area, we discuss four paradigms underlying the scheduling approaches and present several exemplars of each. The four paradigms are: static tabledriven scheduling, static priority preemptive scheduling, dynamic planningbased scheduling, and dynamic best efSort scheduling. In the operating system context, we argue that most of the proprietary commercial kernels as well as realtime extensions to timesharing operating system kernels do not fit the needs of predictable realtime systems. We discuss several research kernels that are currently being built to explicitly meet the needs of realtime applications.
Deterministic JobShop Scheduling: Past, Present and Future
 European Journal of Operational Research
, 1998
"... : Due to the stubborn nature of the deterministic jobshop scheduling problem many solutions proposed are of hybrid construction cutting across the traditional disciplines. The problem has been investigated from a variety of perspectives resulting in several analytical techniques combining generic ..."
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Cited by 65 (2 self)
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: Due to the stubborn nature of the deterministic jobshop scheduling problem many solutions proposed are of hybrid construction cutting across the traditional disciplines. The problem has been investigated from a variety of perspectives resulting in several analytical techniques combining generic as well as problem specific strategies. We seek to assess a subclass of this problem in which the objective is minimising makespan, by providing an overview of the history, the techniques used and the researchers involved. The sense and direction of their work is evaluated by assessing the reported results of their techniques on the available benchmark problems. From these results the current situation and pointers for future work are provided. KEYWORDS: Scheduling Theory; JobShop; Review; Computational Study; 1. INTRODUCTION Current market trends such as consumer demand for variety, shorter product life cycles and competitive pressure to reduce costs have resulted in the need for zero i...
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).
Approximability and Nonapproximability Results for Minimizing Total Flow Time on a Single Machine
, 1995
"... We consider the problem of scheduling n jobs that are released over time on a single machine in order to minimize the total flow time. This problem is wellknown to be NPcomplete, and the best polynomial time approximation algorithms constructed so far had (more or less trivial) worstcase perfor ..."
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Cited by 51 (4 self)
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We consider the problem of scheduling n jobs that are released over time on a single machine in order to minimize the total flow time. This problem is wellknown to be NPcomplete, and the best polynomial time approximation algorithms constructed so far had (more or less trivial) worstcase performance guarantees of O(n). In this paper, we present one positive and one negative result on polynomial time approximations for the minimum total flow time problem: The positive result is the first approximation algorithm with a sublinear worstcase performance guarantee of O( p n). This algorithm is based on resolving the preemptions of the corresponding optimum preemptive schedule. The performance guarantee of our approximation algorithm is not far from best possible as our second, negative, result demonstrates: Unless P = NP , no polynomial time approximation algorithm for minimum total flow time can have a worstcase performance guarantee of O(n 1 2 \Gamma" ) for any " ? 0.
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
Scheduling Hard RealTime Systems: A Review
, 1991
"... Recent results in the application of... this paper. The review takes the form of an analysis of the problems presented by different application requirements and characteristics. Issues covered include uniprocessor and multiprocessor systems, periodic and aperiodic processes, static and dynamic algor ..."
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Cited by 48 (7 self)
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Recent results in the application of... this paper. The review takes the form of an analysis of the problems presented by different application requirements and characteristics. Issues covered include uniprocessor and multiprocessor systems, periodic and aperiodic processes, static and dynamic algorithms, transient overloads and resource usage. Protocols that limit and reduce blocking are discussed. Considerations are also given to scheduling Ada tasks.
Complexity of scheduling multiprocessor tasks with prespecified processor allocations
 DISCRETE APPLIED MATHEMATICS
, 1994
"... ..."
Minimizing Average Completion Time in the Presence of Release Dates
, 1995
"... A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In con ..."
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Cited by 42 (7 self)
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A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NPhard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constantfactor approximation algorithms for several variants of the single and parallel machine model. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of average weighted completion time as well. 1 Introduction Two important characteristics of many realw...
SINGLE MACHINE SCHEDULING WITH RELEASE DATES
, 2002
"... We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a timeindexed formulation, the other on a completiontime formulation. We show their ..."
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Cited by 38 (12 self)
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We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a timeindexed formulation, the other on a completiontime formulation. We show their equivalence by proving that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations. The proof relies on the notion of mean busy times of jobs, a concept which enhances our understanding of these LP relaxations. Based on the greedy solution, we describe two simple randomized approximation algorithms, which are guaranteed to deliver feasible schedules with expected objective function value within factors of 1.7451 and 1.6853, respectively, of the optimum. They are based on the concept of common and independent αpoints, respectively. The analysis implies in particular that the worstcase relative error of the LP relaxations is at most 1.6853, and we provide instances showing thatitis atleaste/(e − 1) ≈ 1.5819. Both algorithms may be derandomized; their deterministic versions run in O(n²) time. The randomized algorithms also apply to the online setting, in which jobs arrive dynamically over time and one must decide which job to process without knowledge of jobs that will be released afterwards.