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Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems
[chapter]
1998
Lecture Notes in Computer Science
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An important class of scheduling problems concerns parallel machines and precedence constraints. ...
We present a 4-approximation algorithm for the total weighted completion time objective for this general class of problems. The algorithm is a rather simple form of list scheduling. ...
They also thank the organizers of the workshop on "Parallel Scheduling" held July 14-18, 1997, at Schloß Dagstuhl, Germany, where this work was initiated. ...
doi:10.1007/3-540-69346-7_28
fatcat:ete2x6a3zfdvngj3cq2c4jvgsy
Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems
[article]
2021
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A well studied and difficult class of scheduling problems concerns parallel machines and precedence constraints. ...
We provide the first constant-factor approximation algorithms for the makespan and the total weighted completion time objectives in this general class of problems. ...
Approximation bounds for a general class of
precedence constrained parallel machine scheduling problems. In R. Bixby, E. A. Boyd, and
R. Z. ...
doi:10.14279/depositonce-14622
fatcat:eai5hnaefjbjzbxchtpg4xmcz4
Page 4073 of Mathematical Reviews Vol. , Issue 82i
[page]
1982
Mathematical Reviews
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“Transformations are developed which systematically reduce the size of the general precedence-constrained problem. ...
A class of problems is studied which includes the least-cost fault detection problem, the one-machine total weighted completion
time problem, and the two-machine maximum flow-time problem. ...
Page 6696 of Mathematical Reviews Vol. , Issue 2000i
[page]
2000
Mathematical Reviews
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
(D-TUB; Berlin) Approximation bounds for a general class of precedence constrained parallel machine scheduling problems. ...
Summary: “A well-studied and difficult class of scheduling prob- lems concerns parallel machines and precedence constraints. ...
Page 8087 of Mathematical Reviews Vol. , Issue 99k
[page]
1999
Mathematical Reviews
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Summary: “We present new approximation algorithms for the problem of scheduling precedence-constrained jobs on parallel machines that are uniformly related. ...
)
literature.
99k:90087 90B35 68M20 68Q25 Chudak, Fabian A. (1-CRNL-ENO; Ithaca, NY); Shmoys, David B. (1-CRNL-ENO; Ithaca, NY) Approximation algorithms for precedence-constrained scheduling problems on ...
Page 4491 of Mathematical Reviews Vol. , Issue 2000f
[page]
2000
Mathematical Reviews
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The author considers the problem of scheduling a set of precedence constrained parallel tasks on a multiprocessor with P processors. ...
be evaluated.”
2000f:90020 90B35 68M20
Li, Keqin (1-SUNYP-CM; New Paltz, NY)
Analysis of the list scheduling algorithm for precedence constrained parallel tasks. ...
An Efficient Approximation Algorithm for Minimizing Makespan on Uniformly Related Machines
[chapter]
1998
Lecture Notes in Computer Science
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We give a new e cient approximation algorithm for scheduling precedence constrained jobs on machines with di erent speeds. The problem is as follows. ...
In the process we also obtain a constant factor approximation algorithm for the special case of precedence constraints induced by a collection of chains. ...
Acknowledgments We thank Monika Henzinger for simplifying the proof of Lemma 2. ...
doi:10.1007/3-540-69346-7_29
fatcat:5lqfbcbehfg6zd7rn7dfajdiau
Page 5102 of Mathematical Reviews Vol. , Issue 96h
[page]
1996
Mathematical Reviews
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Summary: “The problem of scheduling a set of tasks on two parallel and identical processors is considered. The executions of tasks are constrained by precedence relations. ...
Summary: “It is shown that the precedence constrained K-
,
90 ECONOMICS, OPERATIONS RESEARCH, PROGRAMMING, GAMES 5102
processor scheduling problem is hard for the parameterized complexity class W[2]. ...
Page 556 of Mathematical Reviews Vol. , Issue 89A
[page]
1989
Mathematical Reviews
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“In this paper we derive two a priori upper bounds on the costs for a class of production planning problems under the rolling horizon strategy. ...
Summary: “A one-machine scheduling problem with the maxi- mum tardiness criterion, subject to given technological precedence constraints, is generalized to the case when processing times of op- erations ...
Page 5101 of Mathematical Reviews Vol. , Issue 99g
[page]
1999
Mathematical Reviews
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problems, parallel-machine scheduling prob- lems, shop scheduling problems, due-date scheduling problems, batching problems, changeover times and transportation times problems, multi-purpose-machine scheduling ...
Summary: “In this note, we derive the tight worst case bound V6/2+(1/2)* for scheduling with the MULTIFIT heuristic on two parallel uniform machines with k calls of FFD within MUL- TIFIT. ...
On the price of heterogeneity in parallel systems
2006
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures - SPAA '06
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Second, we separate precedence constrained scheduling (PCS) from the scheduling problems with known constant price of heterogeneity by showing that the simulation method can lengthen makespan by a factor ...
Even precedence and resource constrained scheduling-which provide a fairly rich set of constraints that can model, for example, relative ordering of jobs and the requirement of jobs to hold shared locks-have ...
for helpful comments. ...
doi:10.1145/1148109.1148122
dblp:conf/spaa/GodfreyK06
fatcat:miryqlwm3jaytfdljma2sxuwqi
On the Price of Heterogeneity in Parallel Systems
2008
Theory of Computing Systems
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Second, we separate precedence constrained scheduling (PCS) from the scheduling problems with known constant price of heterogeneity by showing that the simulation method can lengthen makespan by a factor ...
Even precedence and resource constrained scheduling-which provide a fairly rich set of constraints that can model, for example, relative ordering of jobs and the requirement of jobs to hold shared locks-have ...
for helpful comments. ...
doi:10.1007/s00224-008-9102-5
fatcat:r5awh6vywnb7bhx3zp3xzf7pu4
A job-shop problem with one additional resource type
2010
Journal of Scheduling
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In a resource-constrained scheduling problem the execution of the jobs requires, in addition to machines, the use of scarce extra resources. ...
Observe that a feasible schedule for JSO(n, p) is also feasible for the standard job shop problem, and satisfies the restriction that at most p machines work simultaneously. ...
Kellerer and Strusevich [20, 21] address a class of parallel machine scheduling problems where additional resources may be required for processing a task. ...
doi:10.1007/s10951-010-0162-4
fatcat:bduzvvan4vfhjhx2bhny5j6wx4
Precedence-Constrained Scheduling of Malleable Jobs with Preemption
[chapter]
2014
Lecture Notes in Computer Science
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Scheduling jobs with precedence constraints on a set of identical machines to minimize the total processing time (makespan) is a fundamental problem in combinatorial optimization. ...
The instantaneous processing rate of a job is a non-decreasing function of the number of machines assigned to it (we call it the processing function). ...
Introduction In the precedence-constrained scheduling problem (we call it the PS problem), the goal is to schedule a set of jobs with precedence constraints on a set of identical machines so as to minimize ...
doi:10.1007/978-3-662-43948-7_68
fatcat:2vgdts2ogfdcpjsy66ini4pcpi
Precedence-constrained Scheduling of Malleable Jobs with Preemption
[article]
2014
arXiv
pre-print
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Scheduling jobs with precedence constraints on a set of identical machines to minimize the total processing time (makespan) is a fundamental problem in combinatorial optimization. ...
The instantaneous processing rate of a job is a non-decreasing function of the number of machines assigned to it (we call it the processing function). ...
Introduction In the precedence-constrained scheduling problem (we call it the PS problem), the goal is to schedule a set of jobs with precedence constraints on a set of identical machines so as to minimize ...
arXiv:1404.6850v1
fatcat:jyxe4cl36fhv7idc4ynbzkuga4
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