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Previous article Next article Bounds on Multiprocessing Timing AnomaliesR. L. GrahamR. L. Grahamhttps: //doi. org/10. 1137/0117039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 E. F. Codd, Multiprogram scheduling. I, II. Introduction and theory, Comm. ACM, 3 (1960), 347–350 10. 1145/367297. 367317 MR0130079 0102. 34202 CrossrefISIGoogle Scholar2 R. L. Graham, Bounds for certain multiprocessing anomalies, Bell System Tech. J. , 45 (1966), 1563–1581 0168. 40703 CrossrefISIGoogle Scholar3 J. Heller, Sequencing aspects of multiprogramming, J. Assoc. Comput. Mach. , 8 (1961), 426–439 MR0159443 CrossrefGoogle Scholar4 John L. Kelley, General topology, D. Van Nostrand Company, Inc. , Toronto-New York-London, 1955xiv+298 MR0070144 0066. 16604 Google Scholar5 B. Liebesman, The use of a special algebra in schedule analysis, to appear Google Scholar6 G. K. Manacher, Production and stabilization of real-time task schedules, J. Assoc. Comput. Mach. , 14 (1967), 439–465 CrossrefISIGoogle Scholar7 B. P. Ochsner, Controlling a multiprocessor system, Record, 44, Bell Laboratories, 1966, pp. 59–62 Google Scholar8 P. Richards, Parallel programming, Rep. , TD-B60-27, Technical Operations Inc. , 1960 Google Scholar9 M. Rothkopf, Scheduling independent tasks on one or more processors, Interim Tech. Rep. , 2, Operations Research Center, M. I. T. , Cambridge, 1964 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails DAG Scheduling and Analysis on Multi-Core Systems by Modelling Parallelism and DependencyIEEE Transactions on Parallel and Distributed Systems, Vol. 33, No. 12 | 1 Dec 2022 Cross Ref The BH-mixed scheduling algorithm for DAG tasks with constrained deadlinesJournal of Systems Architecture, Vol. 131 | 1 Oct 2022 Cross Ref Streaming algorithms for multitasking scheduling with shared processingDiscrete Applied Mathematics, Vol. 320 | 1 Oct 2022 Cross Ref Checkpointing Workflows à la Young/Daly Is Not Good EnoughACM Transactions on Parallel Computing, Vol. 25 | 2 September 2022 Cross Ref Parallel Machine Scheduling Under Uncertainty: Models and Exact AlgorithmsINFORMS Journal on Computing, Vol. 68 | 17 August 2022 Cross Ref EasyFL: A Low-Code Federated Learning Platform for DummiesIEEE Internet of Things Journal, Vol. 9, No. 15 | 1 Aug 2022 Cross Ref Demand-Aware Network Design With 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scheduling on two identical machines with & Industrial Engineering, Vol. | 1 Jun 2020 Cross Ref A genetic algorithm for Management Science, Vol. No. 2 | 27 March Cross Ref Resource Allocation in Low Density Spreading Uplink NOMA via Asymptotic IEEE International Symposium on Information Theory | 1 Jun 2020 Cross Ref Dynamic with Minimal of the on and Analysis of Computing Systems, Vol. No. 1 | 27 May 2020 Cross Ref On scheduling multiple two-stage Computer Science, Vol. | 1 May 2020 Cross Ref Real-Time scheduling and analysis of parallel tasks on heterogeneous of Systems Architecture, Vol. | 1 May 2020 Cross Ref for to for Packing in Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. No. 5 | 1 May 2020 Cross Ref The Efficient Multiprocessor of IEEE International Symposium on Real-Time Distributed Computing | 1 May 2020 Cross Ref Data Services for High Energy International Symposium on Cloud and Internet Computing | 1 May 2020 Cross Ref Analysis of a List 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and of Scheduling, Vol. No. 1 | 28 January 2020 Cross Ref A for Proceedings in Computer Science, Vol. | 20 January 2020 Cross Ref Makespan for Software Testing Under in of Computer Systems and Networks | 12 May Cross Ref Approximation algorithms for & Chemical Engineering, Vol. | 1 Jan 2020 Cross Ref Single with Time for Parallel Task Processing with and Unknown Transactions on Parallel and Distributed Systems, Vol. 31, No. 1 | 1 Jan 2020 Cross Ref An Approximation Algorithm for a Task Sequencing and Scheduling Problem a and | 1 Jan 2020 Cross Ref Greedy Is Optimal for Online Restricted Assignment and Smart Grid Scheduling for Unit Size and Online Algorithms | 25 January 2020 Cross Ref A Parallel Tool for the Simulation and Processing and Applied Mathematics | 19 March 2020 Cross Ref Makespan Minimization for Parallel with Energy Optimization Theory and Operations Research | 29 June 2020 Cross Ref Scheduling to Time via Linear Journal on Computing, Vol. No. 4 | 9 April on Hybrid Improved | 3 December 2020 Cross Ref An of a in Multiple Parallelism on Modern Systems | 1 September 2020 Cross Ref Buffer Minimization with on a in | 23 September 2020 Cross Ref Automated Journal of Vol. 24 | 17 Dec Cross Ref Scheduling of Performance Evaluation Vol. No. 2 | 4 Dec Cross Ref Uniform Parallel Machine Scheduling with Job and Vol. No. 24 | 13 December Cross Ref Modeling and Scheduling Problem with Uniform Parallel to Vol. No. 12 | 21 November Cross Ref Real-Time Scheduling of DAG Tasks with Arbitrary Transactions on Design of Systems, Vol. 24, No. 6 | 14 Nov Cross Ref Scheduling parallel identical machines to parallel approximation of Parallel and Distributed Computing, Vol. | 1 Nov Cross Ref scheduling of independent parallel tasks on and multiple processorsJournal of Parallel and Distributed Computing, Vol. | 1 Nov Cross Ref Minimizing machine over of the scheduling problem Computer Science, Vol. | 1 Nov Cross Ref Performance Tasks with for Cloud Data Center Resource Transactions on Parallel and Distributed Systems, Vol. 30, No. 11 | 1 Nov Cross Ref Response Time Bounds for DAG Parallel Tasks on Heterogeneous Transactions on Parallel and Distributed Systems, Vol. 30, No. 11 | 1 Nov Cross Ref The of and for Network of Operations Research, Vol. 44, No. 4 | 1 Nov Cross Ref Timing-Anomaly Free Dynamic Scheduling of DAG Tasks on Multi-Core Transactions on Embedded Computing Systems, Vol. No. | 19 Oct Cross Ref Two-Aggregator Topology Optimization Using Multiple Paths in Data Center NetworksIEEE Transactions on Cloud Computing, Vol. No. 4 | 1 Oct Cross Ref A of parallel machine scheduling with processing of Scheduling, Vol. No. 5 | 25 March Cross Ref on an of Computer Science, Vol. 13, No. 5 | 17 June Cross Ref On for with of the VLDB Vol. 13, No. 2 | 1 Oct Cross Ref Assignment in Real-Time Scheduling of DAG Tasks on Transactions on Parallel and Distributed Systems, Vol. 30, No. 10 | 1 Oct Cross Ref A of the loop schedulerConcurrency and Computation: Practice and Experience, Vol. 31, No. 18 | 1
Ron Graham (Sat,) studied this question.