77 research outputs found

    Some topics on deterministic scheduling problems

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    Sequencing and scheduling problems are motivated by allocation of limited resources over time. The goal is to find an optimal allocation where optimality is defined by some problem specific objectives. This dissertation considers the scheduling of a set of ri tasks, with precedence constraints, on m \u3e= 1 identical and parallel processors so as to minimize the makespan. Specifically, it considers the situation where tasks, along with their precedence constraints, are released at different times, and the scheduler has to make scheduling decisions without knowledge of future releases. Both preemptive and nonpreemptive schedules are considered. This dissertation shows that optimal online algorithms exist for some cases, while for others it is impossible to have one. The results give a sharp boundary delineating the possible and the impossible cases. Then an O(n log n)-time implementation is given for the algorithm which solves P|pj = 1, rj, outtree| ΣCj and P|pmtn, pj=1,rj,outtree|ΣCj. A fundamental problem in scheduling theory is that of scheduling a set of n unit-execution-time (UET) tasks, with precedence constraints, on m \u3e 1 parallel and identical processors so as to minimize the mean flow time. For arbitrary precedence constraints, this dissertation gives a 2-approximation algorithm. For intrees, a 1.5-approximation algorithm is given. Six dual criteria problems are also considered in this dissertation. Two open problems are first solved. Both problems are single machine scheduling problems with the number of tardy jobs as the primary criterion and with the total completion time and the total tardiness as the secondary criterion, respectively. Both problems are shown to be NP-hard. Then it focuses on bi-criteria scheduling problems involving the number of tardy jobs, the maximum weighted tardiness and the maximum tardiness. NP-hardness proofs are given for the scheduling problems when the number of tardy jobs is the primary criterion and the maximum weighted tardiness is the secondary criterion, or vice versa. It then considers complexity relationships between the various problems, gives polynomial-time algorithms for some special cases, and proposes fast heuristics for the general case

    Static allocation of computation to processors in multicomputers

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    Scheduling task systems with resources.

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    Thesis. 1980. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.Vita.Bibliography: leaves 144-145.Ph.D

    Structural Properties of an Open Problem in Preemptive Scheduling

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    Structural properties of optimal preemptive schedules have been studied in a number of recent papers with a primary focus on two structural parameters: the minimum number of preemptions necessary, and a tight lower bound on `shifts', i.e., the sizes of intervals bounded by the times created by preemptions, job starts, or completions. So far only rough bounds for these parameters have been derived for specific problems. This paper sharpens the bounds on these structural parameters for a well-known open problem in the theory of preemptive scheduling: Instances consist of in-trees of nn unit-execution-time jobs with release dates, and the objective is to minimize the total completion time on two processors. This is among the current, tantalizing `threshold' problems of scheduling theory: Our literature survey reveals that any significant generalization leads to an NP-hard problem, but that any significant simplification leads to tractable problem. For the above problem, we show that the number of preemptions necessary for optimality need not exceed 2n12n-1; that the number must be of order Ω(logn)\Omega(\log n) for some instances; and that the minimum shift need not be less than 22n+12^{-2n+1}. These bounds are obtained by combinatorial analysis of optimal schedules rather than by the analysis of polytope corners for linear-program formulations, an approach to be found in earlier papers. The bounds immediately follow from a fundamental structural property called `normality', by which minimal shifts of a job are exponentially decreasing functions. In particular, the first interval between a preempted job's start and its preemption is a multiple of 1/2, the second such interval is a multiple of 1/4, and in general, the ii-th preemption occurs at a multiple of 2i2^{-i}. We expect the new structural properties to play a prominent role in finally settling a vexing, still-open question of complexity

    Production Scheduling with Complex Precedence Constraints in Parallel Machines

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    Heuristic search is a core area of artificial intelligence and the employment of an efficient search algorithm is critical to the performance of an intelligent system. This paper addresses a production scheduling problem with complex precedence constraints in an identical parallel machines environment. Although this particular problem can be found in several production and other scheduling applications; it is considered to be NP-hard due to its high computational complexity. The solution approach we adopt is based on a comparison among several dispatching rules combined with a diagram analysis methodology. Computational results on large instances provide relatively high quality practical solutions in very short computational times, indicating the applicability of the methodology in real life production scheduling applications

    Scheduling theory since 1981: an annotated bibliography

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    A Survey of Pipelined Workflow Scheduling: Models and Algorithms

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    International audienceA large class of applications need to execute the same workflow on different data sets of identical size. Efficient execution of such applications necessitates intelligent distribution of the application components and tasks on a parallel machine, and the execution can be orchestrated by utilizing task-, data-, pipelined-, and/or replicated-parallelism. The scheduling problem that encompasses all of these techniques is called pipelined workflow scheduling, and it has been widely studied in the last decade. Multiple models and algorithms have flourished to tackle various programming paradigms, constraints, machine behaviors or optimization goals. This paper surveys the field by summing up and structuring known results and approaches
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