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17
Scheduling Split Intervals
, 2002
"... We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t _) 1, a of their segments intersect. Such jobs show up in a I.I Problem Statement and Mo ..."
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Cited by 58 (5 self)
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We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t _) 1, a of their segments intersect. Such jobs show up in a I.I Problem Statement and Motivation. We wide range of applications, including the transmission consider the problem of scheduling jobs that are given of continuousmedia data, allocation of linear resources as groups of nonintersecting segments on the real line. (e.g. bandwidth in linear processor arrays), and in Each job Jj is associated with a tinterval, Ij, which
A Linear Time Approximation Scheme for Job Shop Scheduling
"... In this paper we present a linear time approximation scheme for the nonpreemptive job shop scheduling problem when the number of machines and the number of operations per job are fixed. We also show how to extend the approximation scheme for the preemptive version of the problem. ..."
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Cited by 12 (8 self)
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In this paper we present a linear time approximation scheme for the nonpreemptive job shop scheduling problem when the number of machines and the number of operations per job are fixed. We also show how to extend the approximation scheme for the preemptive version of the problem.
Makespan Minimization in Job Shops: A Linear Time Approximation Schemes
, 1999
"... In this paper we present a linear time approximation scheme for the job shop scheduling problem with fixed number of machines and fixed number of operations per job. Our approximation scheme can be extended to the case of job shop problems with release and delivery times, flexible job shops, dag job ..."
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Cited by 12 (2 self)
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In this paper we present a linear time approximation scheme for the job shop scheduling problem with fixed number of machines and fixed number of operations per job. Our approximation scheme can be extended to the case of job shop problems with release and delivery times, flexible job shops, dag job shops and preemptive variants of these problems.
Grouping techniques for scheduling problems: simpler and faster
 Proceedings of the 9th Annual European Symposium on Algorithms, 2001
, 2001
"... In this paper we describe a general grouping technique to devise faster and simpler approximation schemes for several scheduling problems. We illustrate the technique on two different scheduling problems: scheduling on unrelated parallel machines with costs and the job shop scheduling problem. The t ..."
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Cited by 11 (4 self)
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In this paper we describe a general grouping technique to devise faster and simpler approximation schemes for several scheduling problems. We illustrate the technique on two different scheduling problems: scheduling on unrelated parallel machines with costs and the job shop scheduling problem. The time complexity of the resulting approximation schemes is always linear in the number n of jobs, and the multiplicative constant hidden in the O(n) running time is reasonably small and independent of the error ε. 1
Scheduling on Unrelated Machines under TreeLike Precedence Constraints
"... We present polylogarithmic approximations for the RprecCmax and Rprec  � j wjCj problems, when the precedence constraints are “treelike ” i.e., when the undirected graph underlying the precedences is a forest. These are the first nontrivial generalizations of the job shop scheduling problem to ..."
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Cited by 8 (1 self)
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We present polylogarithmic approximations for the RprecCmax and Rprec  � j wjCj problems, when the precedence constraints are “treelike ” i.e., when the undirected graph underlying the precedences is a forest. These are the first nontrivial generalizations of the job shop scheduling problem to scheduling with precedence constraints that are not just chains. These are also the first nontrivial results for the weighted completion time objective on unrelated machines with precedence constraints of any kind. We obtain improved bounds for the weighted completion time and flow time for the case of chains with restricted assignment this generalizes the job shop problem to these objective functions. We use the same lower bound of “congestion+dilation”, as in other job shop scheduling approaches (e.g. [21]). The first step in our algorithm for the RprecCmax problem with treelike precedences involves using the algorithm of Lenstra, Shmoys and Tardos [13] to obtain a processor assignment with the congestion + dilation value within a constant factor of the optimal. We then show how to generalize the random delays technique of Leighton, Maggs and Rao [14] to the case of trees. For the weighted completion time, we show a certain type of reduction to the makespan problem, which dovetails well with the lower bound we employ for the makespan problem. For the special case of chains, we show a dependent rounding technique which leads to improved bounds on the weighted completion time and new bicriteria bounds for the flow time.
Polynomial time approximation schemes for general multiprocessor job shop scheduling
, 2002
"... ..."
Approximation schemes for job shop scheduling problems with controllable processing times
, 2005
"... In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. The fact that the jobs have controllable processing times means that it is possible to reduce the processing time of the jobs by paying a certain cost. We consider two models ..."
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Cited by 4 (0 self)
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In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. The fact that the jobs have controllable processing times means that it is possible to reduce the processing time of the jobs by paying a certain cost. We consider two models of controllable processing times: continuous and discrete. For both models we present polynomial time approximation schemes when the number of machines and the number of operations per job are fixed.
New and Improved Algorithms for Minsum Shop Scheduling
 Proceedings 11th Annual ACMSIAM Symposium on Discrete Algorithms
, 2000
"... We consider a general class of multiprocessor shop scheduling problems with a minsum objective, and present approximation methods based on linear programming relaxations in the operation completion times. These LP relaxations use new classes of valid inequalities for multistage jobs. We first consid ..."
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Cited by 4 (0 self)
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We consider a general class of multiprocessor shop scheduling problems with a minsum objective, and present approximation methods based on linear programming relaxations in the operation completion times. These LP relaxations use new classes of valid inequalities for multistage jobs. We first consider open shop problems with total weighted job completion time objective. For the nonpreemptive problem Ojj P w j C j , we introduce "LPbased precedence constraints" and derive a 5.83approximation algorithm. For its preemptive version, Ojpmtnj P w j C j , we show that a simple jobbased greedy algorithm, using directly the LP solution, yields a 3approximation. We then consider a general class of multiprocessor shop scheduling problems, preemptive or nonpreemptive, with precedence constraints between operations, with job or operation release dates, and with a general minsum objective. This class of objectives includes, among others, weighted sums of operations completion times, job comp...
Polynomial Time Approximation Schemes for the Multiprocessor Open and Flow Shop Scheduling Problem
 STACS 2000, LNCS 1770
, 2000
"... We investigate the multiprocessor multistage open shop and ow shop scheduling problem. In both problems, there are s stages each consisting of a number m i of parallel identical machines for 1 i s. Each job consists of s operations with one operation for each stage. The goal is to nd a nonpreemp ..."
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Cited by 3 (1 self)
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We investigate the multiprocessor multistage open shop and ow shop scheduling problem. In both problems, there are s stages each consisting of a number m i of parallel identical machines for 1 i s. Each job consists of s operations with one operation for each stage. The goal is to nd a nonpreemptive schedule that minimizes the makespan. We propose polynomial time approximation schemes for the multiprocessor open shop and ow shop scheduling problem when the number of stages s is constant and the numbers of machines m i are nonconstant. 1 Introduction Problem Denition. A ow shop (or open shop) is a multistage production process with the property that all jobs have to pass through the stages. For ow shops the order in which the jobs pass through the stages is the same, whereas for open shops the order is immaterial. There are n jobs J j , with j = 1; : : : ; n, where each job J j consists of s operations O 1j ; : : : ; O sj . The operation O ij , with i = 1; : : : ; s, has ...
Resource Allocation in Networked and Distributed Environments
"... A central challenge in networked and distributed systems is resource management: how can we partition the available resources in the system across competing users, such that individual users are satised and certain systemwide objectives of interest are optimized? In this thesis, we deal with many ..."
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Cited by 1 (0 self)
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A central challenge in networked and distributed systems is resource management: how can we partition the available resources in the system across competing users, such that individual users are satised and certain systemwide objectives of interest are optimized? In this thesis, we deal with many such fundamental and practical resource allocation problems that arise in networked and distributed environments. We invoke two sophisticated paradigms { linear programming and probabilistic methods { and develop provablygood approximation algorithms for a diverse collection of applications. Our main contributions are as follows. 1. Assignment problems: An assignment problem involves a collection of objects and locations, and a load value associated with each objectlocation pair. Our goal is to assign the objects to locations while minimizing various cost functions of the assignment (determined by the load values). This abstract setting models many applications in manufacturing, parallel processing, distributed storage, and wireless networks. We present a single algorithm for assignment which generalizes and unies many classical assignment schemes known in the