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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
Packet routing and jobshop scheduling in O(congestion+dilation) steps
 Combinatorica
, 1994
"... In this paper, we prove that there exists a schedule for routing any set of packets with edgesimple paths, on any network, in O(c+d) steps, where c is the congestion of the paths in the network, and d is the length of the longest path. The result has applications to packet routing in parallel machi ..."
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Cited by 102 (8 self)
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In this paper, we prove that there exists a schedule for routing any set of packets with edgesimple paths, on any network, in O(c+d) steps, where c is the congestion of the paths in the network, and d is the length of the longest path. The result has applications to packet routing in parallel machines, network emulations, and jobshop scheduling.
A PTAS for the Multiple Knapsack Problem
, 1993
"... The Multiple Knapsackproblem (MKP) is a natural and well known generalization of the single knapsack problem and is defined as follows. We are given a set of n items and m bins (knapsacks) such that each item i has a profit p(i) and a size s(i), and each bin j has a capacity c(j). The goal is to fin ..."
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Cited by 97 (2 self)
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The Multiple Knapsackproblem (MKP) is a natural and well known generalization of the single knapsack problem and is defined as follows. We are given a set of n items and m bins (knapsacks) such that each item i has a profit p(i) and a size s(i), and each bin j has a capacity c(j). The goal is to find a subset of items of maximum profit such that they have a feasible packing in the bins. MKP is a special case of the Generalized Assignment problem (GAP) where the profit and the size of an item can vary based on the specific bin that it is assigned to. GAP is APXhard and a 2approximation for it is implicit in the work of Shmoys and Tardos [26], and thus far, this was also the best known approximation for MKP. The main result of this paper is a polynomial time approximation scheme for MKP. Apart from its inherent theoretical interest as a common generalization of the wellstudied knapsack and bin packing problems, it appears to be the strongest special case of GAP that is not APXhard. We substantiate this by showing that slight generalizations of MKP that are very restricted versions of GAP are APXhard. Thus our results help demarcate the boundary at which instances of GAP becomeAPXhard. An interesting and novel aspect of our approach is an approximation preserving reduction from an arbitrary instance of MKP to an instance with O(log n) distinct sizes and profits.
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 89 (7 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...
Improved Approximation Algorithms for Shop Scheduling Problems
, 1994
"... In the job shop scheduling problem we are given m machines and n jobs; a job consists of a sequence of operations, each of which must be processed on a specified machine; the objective is to complete all jobs as quickly as possible. This problem is strongly NPhard even for very restrictive special ..."
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Cited by 82 (7 self)
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In the job shop scheduling problem we are given m machines and n jobs; a job consists of a sequence of operations, each of which must be processed on a specified machine; the objective is to complete all jobs as quickly as possible. This problem is strongly NPhard even for very restrictive special cases. We give the first randomized and deterministic polynomialtime algorithms that yield polylogarithmic approximations to the optimal length schedule. Our algorithms also extend to the more general case where a job is given not by a linear ordering of the machines on which it must be processed but by an arbitrary partial order. Comparable bounds can also be obtained when there are m 0 types of machines, a specified number of machines of each type, and each operation must be processed on one of the machines of a specified type, as well as for the problem of scheduling unrelated parallel machines subject to chain precedence constraints. Key Words: scheduling, approximation algorithms AM...
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...
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 69 (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...
EndtoEnd Scheduling to Meet Deadlines in Distributed Systems
, 1994
"... In a distributed system or communication network tasks may need to be executed on more than one processor. For timecritical tasks, the timing constraints are typically given as endtoend releasetimes and deadlines. This paper describes algorithms to schedule a class of systems where all the tasks ..."
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Cited by 69 (3 self)
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In a distributed system or communication network tasks may need to be executed on more than one processor. For timecritical tasks, the timing constraints are typically given as endtoend releasetimes and deadlines. This paper describes algorithms to schedule a class of systems where all the tasks execute on different processors in turn in the same order. This endtoend scheduling problem is known as the flowshop problem. We present two cases where the problem is tractable and evaluate a heuristic for the N Phard general case. We generalize the traditional flowshop model in two directions. First, we present an algorithm for scheduling flow shops where tasks can be serviced more than once by some processors. Second, we describe a heuristic algorithm to schedule flow shops that consist of periodic tasks. Some considerations are made about scheduling systems with more than one flow shop. 1
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
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