Minimizing total completion time with machine-dependent priority lists

Previous article Next article Bounds on Multiprocessing Timing AnomaliesR. L. GrahamR. L. Grahamhttps://doi.org/10.1137/0117039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. F. Codd, Multiprogram scheduling. I, II. Introduction and theory, Comm. ACM, 3 (1960), 347–350 10.1145/367297.367317 MR0130079 0102.34202 CrossrefISIGoogle Scholar[2] R. L. Graham, Bounds for certain multiprocessing anomalies, Bell System Tech. J., 45 (1966), 1563–1581 0168.40703 CrossrefISIGoogle Scholar[3] J. Heller, Sequencing aspects of multiprogramming, J. Assoc. Comput. Mach., 8 (1961), 426–439 MR0159443 CrossrefGoogle Scholar[4] John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955xiv+298 MR0070144 0066.16604 Google Scholar[5] B. Liebesman, The use of a special algebra in schedule analysis, to appear Google Scholar[6] G. K. Manacher, Production and stabilization of real-time task schedules, J. Assoc. Comput. Mach., 14 (1967), 439–465 CrossrefISIGoogle Scholar[7] B. P. Ochsner, Controlling a multiprocessor system, Record, 44, Bell Laboratories, 1966, pp. 59–62 Google Scholar[8] P. Richards, Parallel programming, Rep., TD-B60-27, Technical Operations Inc., 1960 Google Scholar[9] 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 Minimal Congestion and Route LengthsIEEE/ACM Transactions on Networking, Vol. 30, No. 4 | 1 Aug 2022 Cross Ref Speed scaling scheduling of multiprocessor jobs with energy constraint and makespan criterionJournal of Global Optimization, Vol. 83, No. 3 | 26 November 2021 Cross Ref An Efficient Parallel Algorithm for Detecting Packet Filter ConflictsAlgorithms, Vol. 15, No. 7 | 7 July 2022 Cross Ref A two-stage genetic programming framework for Stochastic Resource Constrained Multi-Project Scheduling Problem under New Project InsertionsApplied Soft Computing, Vol. 124 | 1 Jul 2022 Cross Ref Minimizing makespan on parallel batch processing machines with two-dimensional rectangular jobsComputers & Industrial Engineering, Vol. 169 | 1 Jul 2022 Cross Ref Joinable Parallel Balanced Binary TreesACM Transactions on Parallel Computing, Vol. 9, No. 2 | 30 Jun 2022 Cross Ref Work-conserving disciplines are asymptotic optimal in completion time minimizationIISE Transactions, Vol. 43 | 30 June 2022 Cross Ref Tight approximation bounds for the LPT rule applied to identical parallel machines with small jobsJournal of Scheduling, Vol. 1 | 28 June 2022 Cross Ref A novel genetic algorithm based system for the scheduling of medical treatmentsExpert Systems with Applications, Vol. 195 | 1 Jun 2022 Cross Ref Bounding the execution time of parallel applications on unrelated multiprocessorsReal-Time Systems, Vol. 58, No. 2 | 21 October 2021 Cross Ref Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion timeEuropean Journal of Operational Research, Vol. 52 | 1 Jun 2022 Cross Ref The fellowship of the Dyson ring: ACT&Friends’ results and methods for GTOC 11Acta Astronautica, Vol. 8 | 1 Jun 2022 Cross Ref Efficient Simulation of 3D Reaction-Diffusion in Models of Neurons and NetworksFrontiers in Neuroinformatics, Vol. 16 | 17 May 2022 Cross Ref Malleable scheduling beyond identical machinesJournal of Scheduling, Vol. 12 | 11 May 2022 Cross Ref Faster Minimization of Tardy Processing Time on a Single MachineAlgorithmica, Vol. 84, No. 5 | 27 January 2022 Cross Ref Guaranteeing Safety Despite Physical Errors in Cyber-Physical Systems2022 IEEE 28th Real-Time and Embedded Technology and Applications Symposium (RTAS) | 1 May 2022 Cross Ref Minimizing DAG Utilization by Exploiting SMT2022 IEEE 28th Real-Time and Embedded Technology and Applications Symposium (RTAS) | 1 May 2022 Cross Ref Response time analysis of parallel tasks on accelerator-based heterogeneous platformsJournal of Systems Architecture, Vol. 126 | 1 May 2022 Cross Ref Out-of-Core Edge Partitioning at Linear Run-Time2022 IEEE 38th International Conference on Data Engineering (ICDE) | 1 May 2022 Cross Ref Variable neighbourhood search for job scheduling with position-dependent deteriorating processing timesJournal of the Operational Research Society, Vol. 131 | 26 April 2022 Cross Ref On the Evaluation of the Ambulance Capacity of the Asian Side of Istanbul in the Case of a Serious EarthquakeDisaster Medicine and Public Health Preparedness, Vol. 16, No. 2 | 27 October 2020 Cross Ref An adaptive self‐scheduling loop schedulerConcurrency and Computation: Practice and Experience, Vol. 34, No. 6 | 2 December 2021 Cross Ref Semi-online scheduling: A surveyComputers & Operations Research, Vol. 139 | 1 Mar 2022 Cross Ref Multi-station test scheduling optimization method for industrial robot servo systemJournal of Ambient Intelligence and Humanized Computing, Vol. 13, No. 3 | 15 October 2020 Cross Ref Computing exact WCRT for typed DAG tasks on heterogeneous multi-core processorsJournal of Systems Architecture, Vol. 124 | 1 Mar 2022 Cross Ref Effects of Continuous vs Discrete Frequency Scaling and Core Allocation on Energy Efficiency of Static Schedules for Moldable TasksParallel Processing Letters, Vol. 32, No. 01n02 | 10 December 2021 Cross Ref Single-machine scheduling with machine unavailability periods and resource dependent processing timesEuropean Journal of Operational Research, Vol. 296, No. 2 | 1 Jan 2022 Cross Ref The Piggyback Transportation Problem: Transporting drones launched from a flying warehouseEuropean Journal of Operational Research, Vol. 296, No. 2 | 1 Jan 2022 Cross Ref A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular PenaltiesMathematics, Vol. 10, No. 1 | 25 December 2021 Cross Ref Scheduling of Real-Time Tasks With Multiple Critical Sections in Multiprocessor SystemsIEEE Transactions on Computers, Vol. 71, No. 1 | 1 Jan 2022 Cross Ref Noncooperative Supply Chain SchedulingSupply Chain Scheduling | 20 October 2021 Cross Ref Saving power in disks, flash memories, and serversStorage Systems | 1 Jan 2022 Cross Ref BibliographyStorage Systems | 1 Jan 2022 Cross Ref A 2-Competitive Largest Job on Least Loaded Machine Online Algorithm Based on the Multi List Scheduling ModelProceedings of the Seventh International Conference on Mathematics and Computing | 6 March 2022 Cross Ref New Results on Competitive Analysis of Online SRPT SchedulingProceedings of the Seventh International Conference on Mathematics and Computing | 6 March 2022 Cross Ref Scheduling K-mers Counting in a Distributed EnvironmentOptimization in Artificial Intelligence and Data Sciences | 2 March 2022 Cross Ref A Parallel Algorithm for GAC Filtering of the Alldifferent ConstraintIntegration of Constraint Programming, Artificial Intelligence, and Operations Research | 10 June 2022 Cross Ref Exploring Scheduling Algorithms for Parallel Task Graphs: A Modern Game Engine Case StudyEuro-Par 2022: Parallel Processing | 1 August 2022 Cross Ref Approximation Schemes for Machine SchedulingOperations Research Proceedings 2021 | 30 August 2022 Cross Ref Approximation Scheme for Single-Machine Rescheduling with Job Delay and RejectionAlgorithmic Aspects in Information and Management | 18 September 2022 Cross Ref The Constrained Parallel-Machine Scheduling Problem with Divisible Processing Times and PenaltiesAlgorithmic Aspects in Information and Management | 18 September 2022 Cross Ref PathTracer: Understanding Response Time of Signal Processing Applications on Heterogeneous MPSoCsACM Transactions on Modeling and Performance Evaluation of Computing Systems, Vol. 6, No. 4 | 31 Dec 2021 Cross Ref Energy-efficient scheduling: classification, bounds, and algorithmsSādhanā, Vol. 46, No. 1 | 26 February 2021 Cross Ref A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operatorsFlexible Services and Manufacturing Journal, Vol. 33, No. 4 | 28 November 2020 Cross Ref Improved scalability of demand-aware datacenter topologies with minimal route lengths and congestionPerformance Evaluation, Vol. 152 | 1 Dec 2021 Cross Ref Online Makespan Scheduling with Job Migration on Uniform MachinesAlgorithmica, Vol. 83, No. 12 | 19 August 2021 Cross Ref Opportunistic Overlapping: Joint scheduling of uplink URLLC/eMBB traffic in NOMA based Wireless Systems2021 19th International Symposium on Modeling and Optimization in Mobile, Ad hoc, and Wireless Networks (WiOpt) | 18 Oct 2021 Cross Ref A note on labeling methods to schedule unit execution time tasks in the presence of delayed precedence constraintsJournal of Parallel and Distributed Computing, Vol. 156 | 1 Oct 2021 Cross Ref Bounding schemes for the parallel machine scheduling problem with DeJong's learning effectJournal of Parallel and Distributed Computing, Vol. 156 | 1 Oct 2021 Cross Ref Mixed-Cell-Height Detailed Placement Considering Complex Minimum-Implant-Area ConstraintsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 40, No. 10 | 1 Oct 2021 Cross Ref Simulation-based priority rules for the stochastic resource-constrained net present value and risk problemComputers & Industrial Engineering, Vol. 160 | 1 Oct 2021 Cross Ref Cost-adaptive multi-class multicast service aggregation based on distributed sub-trees in elastic optical data center networksOptical Fiber Technology, Vol. 66 | 1 Oct 2021 Cross Ref Delay and Cost Optimization in Computational Offloading Systems with Unknown Task Processing TimesIEEE Transactions on Cloud Computing, Vol. 9, No. 4 | 1 Oct 2021 Cross Ref Lap: A latency‐aware parallelism framework for content‐based publish/subscribe systemsConcurrency and Computation: Practice and Experience, Vol. 35 | 21 September 2021 Cross Ref Improved co-scheduling of multi-layer printing path scanning for collaborative additive manufacturingIISE Transactions, Vol. 53, No. 9 | 17 September 2020 Cross Ref Approximation algorithms for makespan minimization on identical parallel machines under resource constraintsJournal of the Operational Research Society, Vol. 72, No. 9 | 23 June 2020 Cross Ref Best Fit Bin Packing with Random Order RevisitedAlgorithmica, Vol. 83, No. 9 | 1 July 2021 Cross Ref Approximation algorithms for the multiprocessor scheduling with submodular penaltiesOptimization Letters, Vol. 15, No. 6 | 20 March 2021 Cross Ref An improved parametric algorithm on two-machine scheduling with given lower and upper bounds for the total processing timeTheoretical Computer Science, Vol. 880 | 1 Aug 2021 Cross Ref Greedy is Optimal for Online Restricted Assignment and Smart Grid Scheduling for Unit Size JobsTheory of Computing Systems, Vol. 65, No. 6 | 8 April 2021 Cross Ref Single Machine Vector Scheduling with General PenaltiesMathematics, Vol. 9, No. 16 | 17 August 2021 Cross Ref A Survey on Problem Formulations and (Meta)Heuristic-Based Solutions in Automated Assembly of Parallel Test FormsInternational Journal of Software Engineering and Knowledge Engineering, Vol. 31, No. 08 | 14 September 2021 Cross Ref Timing-Anomaly Free Dynamic Scheduling of Periodic DAG Tasks with Non-Preemptive Nodes2021 IEEE 27th International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA) | 1 Aug 2021 Cross Ref Graph-Based Optimizations for Multiprocessor Nested Resource Sharing2021 IEEE 27th International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA) | 1 Aug 2021 Cross Ref Greedy Successive Relaying for the Multicarrier Diamond Relay Channel2021 National Conference on Communications (NCC) | 27 Jul 2021 Cross Ref Buffer minimization with conflicts on a lineTheoretical Computer Science, Vol. 876 | 1 Jul 2021 Cross Ref ARTful: A model for user‐defined schedulers targeting multiple high‐performance computing runtime systemsSoftware: Practice and Experience, Vol. 51, No. 7 | 4 April 2021 Cross Ref In-Memory Interval JoinsThe VLDB Journal, Vol. 30, No. 4 | 8 April 2021 Cross Ref Efficient Pre-Solve Algorithms for the Schwerin and Falkenauer_U Bin Packing Benchmark Problems for Getting Optimal Solutions with High ProbabilityMathematics, Vol. 9, No. 13 | 1 July 2021 Cross Ref Teaching Complex Scheduling Algorithms2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) | 1 Jun 2021 Cross Ref Makespan minimization with OR-precedence constraintsJournal of Scheduling, Vol. 24, No. 3 | 29 May 2021 Cross Ref Implementing synchronous reactive components upon multiprocessor platformsJournal of Systems Architecture, Vol. 116 | 1 Jun 2021 Cross Ref Offline preemptive bottom left decreasing height scheduling of power loads in smart gridsEnergy Systems, Vol. 9 | 31 May 2021 Cross Ref Disruption-Free Load Balancing for Aerial Access NetworkWireless Communications and Mobile Computing, Vol. 2021 | 23 May 2021 Cross Ref K‐ear: Extracting data access periodic characteristics for energy‐aware data clustering and storing in cloud storage systemsConcurrency and Computation: Practice and Experience, Vol. 33, No. 9 | 30 November 2020 Cross Ref Absolute bounds of list algorithms for parallel machines scheduling with unavailability periodsInternational Transactions in Operational Research, Vol. 28, No. 3 | 30 August 2018 Cross Ref Argus: Efficient Job Scheduling in RDMA-assisted Big Data Processing2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS) | 1 May 2021 Cross Ref Iterative job splitting algorithms for parallel machine scheduling with job splitting and setup resource constraintsJournal of the Operational Research Society, Vol. 72, No. 4 | 6 February 2020 Cross Ref Ideal schedules in parallel machine settingsEuropean Journal of Operational Research, Vol. 290, No. 2 | 1 Apr 2021 Cross Ref Exact lexicographic scheduling and approximate reschedulingEuropean Journal of Operational Research, Vol. 290, No. 2 | 1 Apr 2021 Cross Ref Approximate and robust bounded job start scheduling for Royal Mail delivery officesJournal of Scheduling, Vol. 24, No. 2 | 21 March 2021 Cross Ref Two-Aggregator Topology Optimization Using Single Paths in Data Center NetworksIEEE Transactions on Cloud Computing, Vol. 9, No. 2 | 1 Apr 2021 Cross Ref Continuously Bulk Loading over Range Partitioned Tables for Large Scale Historical Data2021 IEEE 37th International Conference on Data Engineering (ICDE) | 1 Apr 2021 Cross Ref Automatic detection of the best performing priority rule for the resource-constrained project scheduling problemExpert Systems with Applications, Vol. 167 | 1 Apr 2021 Cross Ref A hyper-heuristic based ensemble genetic programming approach for stochastic resource constrained project scheduling problemExpert Systems with Applications, Vol. 167 | 1 Apr 2021 Cross Ref Relative Worst-order AnalysisACM Computing Surveys, Vol. 54, No. 1 | 1 Apr 2021 Cross Ref A mixed-integer linear programming model to solve the Multidimensional Multi-Way Number Partitioning ProblemComputers & Operations Research, Vol. 127 | 1 Mar 2021 Cross Ref Capacity Approaching Low Density Spreading in Uplink NOMA via Asymptotic AnalysisIEEE Transactions on Communications, Vol. 69, No. 3 | 1 Mar 2021 Cross Ref Maximin share guarantee for goods with positive externalitiesSocial Choice and Welfare, Vol. 56, No. 2 | 27 August 2020 Cross Ref Scheduling uniform parallel dedicated machines with job splitting, sequence-dependent setup times, and multiple serversComputers & Operations Research, Vol. 126 | 1 Feb 2021 Cross Ref Efficient Hybrid Density Functional Calculations for Large Periodic Systems Using Numerical Atomic OrbitalsJournal of Chemical Theory and Computation, Vol. 17, No. 1 | 14 December 2020 Cross Ref Mixed coordination mechanisms for scheduling games on hierarchical machinesInternational Transactions in Operational Research, Vol. 28, No. 1 | 25 May 2018 Cross Ref Integrated Scheduling of Tasks and Preventive Maintenance Periods in a Parallel Machine Environment With Single Robot ServerIEEE Access, Vol. 9 | 1 Jan 2021 Cross Ref Scheduling ortsfester GebrauchsfaktorenProduktionstheorie 4 | 17 May 2021 Cross Ref Schedule Explainer: An Argumentation-Supported Tool for Interactive Explanations in Makespan SchedulingExplainable and Transparent AI and Multi-Agent Systems | 17 July 2021 Cross Ref Update on the Asymptotic Optimality of LPTEuro-Par 2021: Parallel Processing | 25 August 2021 Cross Ref A Log-Linear $$(2 +5/6)$$-Approximation Algorithm for Parallel Machine Scheduling with a Single Orthogonal ResourceEuro-Par 2021: Parallel Processing | 25 August 2021 Cross Ref Scheduling with Testing on Multiple Identical Parallel MachinesAlgorithms and Data Structures | 31 July 2021 Cross Ref A Fluid Scheduling Algorithm for DAG Tasks with Constrained or Arbitrary DeadlinesIEEE Transactions on Computers | 1 Jan 2021 Cross Ref Improved MapReduce Load Balancing through Distribution-Dependent Hash Function Optimization2020 IEEE 26th International Conference on Parallel and Distributed Systems (ICPADS) | 1 Dec 2020 Cross Ref An exact algorithm for identical parallel machine scheduling under scenarios2020 3rd World Conference on Mechanical Engineering and Intelligent Manufacturing (WCMEIM) | 1 Dec 2020 Cross Ref Vector scheduling with rejection on two machinesInternational Journal of Computer Mathematics, Vol. 97, No. 12 | 9 January 2020 Cross Ref Anomalies in Special Permutation Flow Shop Scheduling ProblemsChinese Journal of Mechanical Engineering, Vol. 33, No. 1 | 9 June 2020 Cross Ref DAG Scheduling and Analysis on Multiprocessor Systems: Exploitation of Parallelism and Dependency2020 IEEE Real-Time Systems Symposium (RTSS) | 1 Dec 2020 Cross Ref High-performance computing under availability constraints to solve dense triangular system2020 5th International Conference on Cloud Computing and Artificial Intelligence: Technologies and Applications (CloudTech) | 24 Nov 2020 Cross Ref Adversarial Attacks in a Deep Reinforcement Learning based Cluster Scheduler2020 28th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS) | 17 Nov 2020 Cross Ref Fast load balance parallel graph analytics with an automatic graph data structure selection algorithmFuture Generation Computer Systems, Vol. 112 | 1 Nov 2020 Cross Ref Influential nodes selection to enhance data dissemination in mobile social networks: A surveyJournal of Network and Computer Applications, Vol. 169 | 1 Nov 2020 Cross Ref Scheduling jobs with sizes and delivery times on identical parallel batch Computer Science, Vol. | 1 Nov 2020 Cross Ref A of optimal multiprocessor schedules and of Combinatorial Optimization, Vol. 40, No. 4 | 12 August 2020 Cross Ref Scheduling on with IEEE Symposium on of Computer | 1 Nov 2020 Cross Ref the for Makespan Scheduling via of Operations Research, Vol. No. 4 | 1 Nov 2020 Cross Ref Parallel of with Parallel for IEEE International Conference on Systems, and | 11 Oct 2020 Cross Ref A approximation framework for and resource Journal of Operational Research, Vol. No. 1 | 1 Oct 2020 Cross Ref Approximation Algorithms for the Submodular Load Balancing with Submodular PenaltiesMathematics, Vol. No. 10 | 15 October 2020 Cross Ref Real-Time Scheduling and Analysis of DAG Tasks Nested Transactions on Computers, Vol. 69, No. 9 | 1 2020 Cross Ref Efficient Federated Scheduling for Parallel Real-Time IEEE 26th International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA) | 1 Aug 2020 Cross Ref On the Asymptotic Optimality of in Time International Conference on Computer Communications and Networks | 1 Aug 2020 Cross Ref Approximation for Scheduling on Parallel with or Problems New Applications and | 8 July 2020 Cross Ref Research on and for the of Job Shop Scheduling Problems in Engineering, Vol. 2020 | 6 Jul 2020 Cross Ref Scheduling on of Computing Surveys, Vol. 53, No. 3 | 5 Jul 2020 Cross Ref Scheduling for the Algorithms and IEEE Symposium on Computers and Communications | 1 Jul 2020 Cross Ref Scheduling MapReduce on Identical and of Computing Systems, Vol. No. 5 | 29 November Cross Ref Optimal scheduling of parallel real-time Systems, Vol. 56, No. 3 | 29 March 2020 Cross Ref On of Transactions on the Vol. No. 3 | 21 Jun 2020 Cross Ref Exact and heuristic algorithms for 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 Scheduling Algorithm for Task on of IEEE International Parallel and Distributed Processing Symposium (IPDPS) | 1 May 2020 Cross Ref On the of DAG Scheduling in Multiprocessor IEEE International Parallel and Distributed Processing Symposium (IPDPS) | 1 May 2020 Cross Ref Joint Task Scheduling and Management in IEEE International Parallel and Distributed Processing Symposium (IPDPS) | 1 May 2020 Cross Ref Machine scheduling with precedence Journal of Operational Research, Vol. No. 2 | 1 Apr 2020 Cross Ref of Parallel and Distributed Computing, Vol. | 1 Apr 2020 Cross Ref The Processing Time rule for identical parallel machines of Scheduling, Vol. No. 2 | 18 December 2018 Cross Ref of for task on machinesJournal of Combinatorial Optimization, Vol. | 6 March 2020 Cross Ref Transactions on Vol. 16, No. 1 | 5 Mar 2020 Cross Ref Improved approximation algorithms for two-stage scheduling Computer Science, Vol. | 1 Feb 2020 Cross Ref for Mixed Vol. No. 1 | 15 May Cross Ref A of of scheduling: 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

We study the problem of designing truthful algorithms for scheduling a set of tasks, each one owned by a selfish agent, to a set of parallel (identical or unrelated) machines in order to minimize the makespan. We consider the following process: at first the agents declare the length of their tasks, then given these bids the protocol schedules the tasks on the machines. The aim of the protocol is to minimize the makespan, i.e. the maximal completion time of the tasks, while the objective of each agent is to minimize the completion time of its task and thus an agent may lie if by doing so, his task may finish earlier. In this paper, we show the existence of randomized truthful (non-polynomial-time) algorithms with expected approximation ratio equal to 3/2 for different scheduling settings (identical machines with and without release dates and unrelated machines) and models of execution (strong or weak). Our result improves the best previously known result [1] for the problem with identical machines (P||C max ) in the strong model of execution and reaches, asymptotically, the lower bound of [5]. In addition, this result can be transformed to a polynomial-time truthful randomized algorithm with expected approximation ratio 3/2+e (resp. $\frac{11}{6}-\frac{1}{3m}$) for Pm||C max (resp. P||C max ).

This paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph equivalent to a collection of disjoint cliques. No two jobs in a clique are allowed to be assigned to the same machine. Scheduling with incompatibilities between jobs represents a well-established line of research in scheduling theory and the case of disjoint cliques has received increasing attention in recent years. While the research up to this point has been focused on the makespan objective, we broaden the scope and study the classical total completion time criterion. In the setting without incompatibilities, this objective is well-known to admit polynomial time algorithms even for unrelated machines via matching techniques. We show that the introduction of incompatibility cliques results in a richer, more interesting picture. We prove that scheduling on identical machines remains solvable in polynomial time, while scheduling on unrelated machines becomes APX-hard. Next, we study the problem under the paradigm of fixed-parameter tractable algorithms (FPT). In particular, we consider a problem variant with assignment restrictions for the cliques rather than the jobs. We prove that, despite still being APX-hard, it can be solved in FPT time with respect to the number of cliques. Moreover, we show that the problem on unrelated machines can be solved in FPT time for reasonable parameters, in particular, the parameter combination: maximum processing time, number of job kinds, and number of machines or maximum processing time, number of job kinds, and number of cliques. The latter results are extensions of known results for the case without incompatibilities, and can even be further extended to the case of total weighted completion time. All of the FPT results make use of n-fold Integer Programs that recently received great attention by proving their usefulness for scheduling problems.

Modern data centers face a key challenge of effectively serving user requests that arrive online. Such requests are inherently multidimensional and characterized by demand vectors over multiple resources such as processor cycles, storage space, and network bandwidth. Typically, different resources require different objectives to be optimized, and $L_r$ norms of loads are among the most popular objectives considered. Furthermore, the server clusters are also often heterogeneous making the scheduling problem more challenging. To address these problems, we consider the online vector scheduling problem in this paper. Introduced by Chekuri and Khanna in 2006, vector scheduling is a generalization of classical load balancing, where every job has a vector load instead of a scalar load. The scalar problem, introduced by Graham in 1966, and its many variants (identical and unrelated machines, makespan and $L_r$ norm optimization, offline and online jobs, etc.) have been extensively studied over the last 50 years. In this paper, we resolve the online complexity of the vector scheduling problem and its important generalizations---for all $L_r$ norms and in both the identical and unrelated machines settings. For an instance with $m$ machines and $d$ dimensions, our main results are: For identical machines, we show that the optimal competitive ratio is $\Theta(\log d / \log \log d)$ by giving an online lower bound and an algorithm with an asymptotically matching competitive ratio. The lower bound is technically challenging, and is obtained via an online lower bound for the minimum monochromatic clique problem using a novel online coloring game and randomized coding scheme. Our techniques also extend to asymptotically tight upper and lower bounds for general $L_r$ norms. For unrelated machines, we show that the optimal competitive ratio is $\Theta(\log m + \log d)$ by giving an online lower bound that matches a previously known upper bound. Unlike identical machines, however, extending these results, particularly the upper bound, to general $L_r$ norms requires new ideas. In particular, we use a carefully constructed potential function that balances the individual $L_r$ objectives with the overall (convexified) min-max objective to guide the online algorithm and track the changes in potential to bound the competitive ratio.

Modern data centers face a key challenge of effectively serving user requests that arrive online. Such requests are inherently multi-dimensional and characterized by demand vectors over multiple resources such as processor cycles, storage space, and network bandwidth. Typically, different resources require different objectives to be optimized, and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> norms of loads are among the most popular objectives considered. Furthermore, the server clusters are also often heterogeneous making the scheduling problem more challenging. To address these problems, we consider the online vector scheduling problem in this paper. Introduced by Chekuri and Khanna (SIAM J. of Comp. 2006), vector scheduling is a generalization of classical load balancing, where every job has a vector load instead of a scalar load. The scalar problem, introduced by Graham in 1966, and its many variants (identical and unrelated machines, makespan and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> -norm optimization, offline and online jobs, etc.) have been extensively studied over the last 50 years. In this paper, we resolve the online complexity of the vector scheduling problem and its important generalizations - for all L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> norms and in both the identical and unrelated machines settings. Our main results are: · For identical machines, we show that the optimal competitive ratio is Θ(log d/ log log d) by giving an online lower bound and an algorithm with an asymptotically matching competitive ratio. The lower bound is technically challenging, and is obtained via an online lower bound for the minimum mono-chromatic clique problem using a novel online coloring game and randomized coding scheme. Our techniques also extend to asymptotically tight upper and lower bounds for general L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> norms. · For unrelated machines, we show that the optimal competitive ratio is Θ(log m + log d) by giving an online lower bound that matches a previously known upper bound. Unlike identical machines, however, extending these results, particularly the upper bound, to general L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> norms requires new ideas. In particular, we use a carefully constructed potential function that balances the individual L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> objectives with the overall (convexified) min-max objective to guide the online algorithm and track the changes in potential to bound the competitive ratio.

Linked articles: COVID‐19 SPECIAL FORUM. J Eur Acad Dermatol Venereol 2020; 34: e241–e255.

We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine is specified by an arbitrary vector) at the other end. While the problem is strongly NP-hard even in the case of a single machine, constant factor approximation algorithms are known for even the most general machine environment of unrelated machines. Recently a PTAS was discovered for the case of identical parallel machines [1]. In contrast, the problem is MAX SNP-hard for unrelated machines [11]. An important open problem was to determine the approximability of the intermediate case of uniformly related machines where each machine has a speed and it takes p=s time to process a job of size p on a machine with speed s. We resolve the complexity of this problem by obtaining a PTAS. This improves the earlier known approximation ratio of (2 + ∈).

Consider n independent jobs and m identical machines in parallel. Job j has a processing time pj and a deadline $\bar{d}_j$. It must complete its processing before or at its deadline. All jobs are available for processing at time t=0 and preemptions are allowed. A set of jobs is said to be feasible if there exists a schedule that meets all the deadlines; such a schedule is called a feasible schedule. Given a feasible set of jobs, our goal is to find a schedule that minimizes the total completion time $\sum C_j$. In the classical $\alpha \mid \beta \mid \gamma$ scheduling notation this problem is referred to as $P \mid prmt, \bar{d}_j \mid \sum C_j$. Lawler (Recent Results in the Theory of Machine Scheduling, in Mathematical Programming: The State of the Art, A. Bachem, M. Grötschel, and B. Korte, eds., Springer, Berlin, 1982, pp. 202-234) raised the question of whether or not the problem is NP-hard. In this paper we present a polynomial-time algorithm for every $m \ge 2$, and we show that the more general problem with m unrelated machines, i.e., $R \mid prmt, \bar{d}_j \mid \sum C_j$, is strongly NP-hard.

In this paper, unrelated parallel machine scheduling problem with job rejection and earliness-tardiness penalties is investigated. The objective is to minimize the total penalty cost by deciding job acceptance, assigning jobs on unrelated machines, and determining the processing sequence of jobs on each machine. To solve this problem, a mixed integer programming (MIP) model is established, and a hybrid genetic algorithm which hybridizes Genetic Algorithm (GA) and tabu search (TS) with a concise encoding method, special genetic operators is proposed. Computational experiments are performed on three different sized sets of test instances which are randomly generated, and the results of comparative experiment demonstrate that the algorithm proposed in this paper can effectively solve the problem.

Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion time

In this paper, we consider the problem of scheduling a set of jobs having only two possible processing times on a set of unrelated parallel machines. This problem is a generalisation of the much more common problem of scheduling equal-length jobs on identical machines. Such a situation may occur in the production of two different types of products. First, we show that an earlier open problem of scheduling jobs with two possible processing times and on unrelated machines with the objective to minimise the makespan can be polynomially solved by an algorithm consisting of two phases. A slight modification of this algorithm yields an absolute worst-case error of for the case of two arbitrary processing times and , . Thus, for practical problems of a large size with two types of products and two possible processing times, the approximation algorithm generates schedules very close to an optimal one.

We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a nonpreemptive schedule that maximizes the weight of jobs that meet their respective deadlines. We give constant factor approximation algorithms for four variants of the problem, depending on the type of the machines (identical vs. unrelated) and the weight of the jobs (identical vs. arbitrary). All these variants are known to be NP-hard, and the two variants involving unrelated machines are also MAX-SNP hard. The specific results obtained are as follows: For identical job weights and unrelated machines: a greedy 2-approximation algorithm. For identical job weights and k identical machines: the same greedy algorithm achieves a tight $\frac{(1+1/k)^k}{(1+1/k)^k-1}$ approximation factor. For arbitrary job weights and a single machine: an LP formulation achieves a 2-approximation for polynomially bounded integral input and a 3-approximation for arbitrary input. For unrelated machines, the factors are 3 and 4, respectively. For arbitrary job weights and k identical machines: the LP-based algorithm applied repeatedly achieves a $\frac{(1+1/k)^k}{(1+1/k)^k-1}$ approximation factor for polynomially bounded integral input and a $\frac{(1+1/2k)^k}{(1+1/2k)^k-1}$ approximation factor for arbitrary input. For arbitrary job weights and unrelated machines: a combinatorial $(3+2\sqrt{2} \approx 5.828)$-approximation algorithm.

Randomized truthful algorithms for scheduling selfish tasks on parallel machines

We introduce and study a general scheduling problem that we term the Packing Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes; a scheduler can process job j at rate xj, subject to arbitrary packing constraints over the set of rates (x) of the outstanding jobs. The PSP framework captures a variety of scheduling problems, including the classical problems of unrelated machines scheduling, broadcast scheduling, and scheduling jobs of different parallelizability. It also captures scheduling constraints arising in diverse modern environments ranging from individual computer architectures to data centers. More concretely, PSP models multidimensional resource requirements and parallelizability, as well as network bandwidth requirements found in data center scheduling. In this paper, we design non-clairvoyant online algorithms for PSP and its special cases -- in this setting, the scheduler is unaware of the sizes of jobs. Our results are summarized as follows. • For minimizing total weighted completion time, we show a O(1)-competitive algorithm. Surprisingly, we achieve this result by applying the well-known Proportional Fairness algorithm (PF) to perform allocations each time instant. Though PF has been extensively studied in the context of maximizing fairness in resource allocation, we present the first analysis in adversarial and general settings for optimizing job latency. Our result is also the first O(1)-competitive algorithm for weighted completion time for several classical non-clairvoyant scheduling problems. •For minimizing total weighted flow time, for any constant e > 0, any O(n1---e)-competitive algorithm requires extra speed (resource augmentation) compared to the offline optimum. We show that PF is a O(log n)-speed O(log n)-competitive non-clairvoyant algorithm, where n is the total number of jobs. We further show that there is an instance of PSP for which no non-clairvoyant algorithm can be O(n1---e)-competitive with o(√log n) speed. •For the classical problem of minimizing total flow time for unrelated machines in the non-clairvoyant setting, we present the first online algorithm which is scalable ((1 + e)-speed O(1)-competitive for any constant e > 0). No non-trivial results were known for this setting, and the previous scalable algorithm could handle only related machines. We develop new algorithmic techniques to handle the unrelated machines setting that build on a new single machine scheduling policy. Since unrelated machine scheduling is a special case of PSP, when contrasted with the lower bound for PSP, our result also shows that PSP is significantly harder than perhaps the most general classical scheduling settings. Our results for PSP show that instantaneous fair scheduling algorithms can also be effective tools for minimizing the overall job latency, even when the scheduling decisions are non-clairvoyant and constrained by general packing constraints.

A Stochastically Perturbed Particle Swarm Optimization for Identical Parallel Machine Scheduling Problems