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Author: Brian Christopher Dean
Publisher:
ISBN:
Category :
Languages : en
Pages : 113
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Book Description
In this dissertation we study a broad class of stochastic scheduling problems characterized by the presence of hard deadline constraints. The input to such a problem is a set of jobs, each with an associated value, processing time, and deadline. We would like to schedule these jobs on a set of machines over time. In our stochastic setting, the processing time of each job is random, known in advance only as a probability distribution (and we make no assumptions about the structure of this distribution). Only after a job completes do we know its actual "instantiated" processing time with certainty. Each machine can process only a singe job at a time, and each job must be assigned to only one machine for processing. After a job starts processing we require that it must be allowed to complete - it cannot be canceled or "preempted" (put on hold and resumed later). Our goal is to devise a scheduling policy that maximizes the expected value of jobs that are scheduled by their deadlines. A scheduling policy observes the state of our machines over time, and any time a machine becomes available for use, it selects a new job to execute on that machine. Scheduling policies can be classified as adaptive or non-adaptive based on whether or not they utilize information learned from the instantiation of processing times of previously-completed jobs in their future scheduling decisions. A novel aspect of our work lies in studying the benefit one can obtain through adaptivity, as we show that for all of our stochastic scheduling problems, adaptivity can only allow us to improve the expected value obtained by an optimal policy by at most a small constant factor. All of the problems we consider are at least NP-hard since they contain the deterministic 0/1 knapsack problem as a special case. We therefore seek to develop approximation algorithms: algorithms that run in polynomial time and compute a policy whose expected value is provably close to that of an optimal adaptive policy.
Author: Brian Christopher Dean
Publisher:
ISBN:
Category :
Languages : en
Pages : 113
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Book Description
In this dissertation we study a broad class of stochastic scheduling problems characterized by the presence of hard deadline constraints. The input to such a problem is a set of jobs, each with an associated value, processing time, and deadline. We would like to schedule these jobs on a set of machines over time. In our stochastic setting, the processing time of each job is random, known in advance only as a probability distribution (and we make no assumptions about the structure of this distribution). Only after a job completes do we know its actual "instantiated" processing time with certainty. Each machine can process only a singe job at a time, and each job must be assigned to only one machine for processing. After a job starts processing we require that it must be allowed to complete - it cannot be canceled or "preempted" (put on hold and resumed later). Our goal is to devise a scheduling policy that maximizes the expected value of jobs that are scheduled by their deadlines. A scheduling policy observes the state of our machines over time, and any time a machine becomes available for use, it selects a new job to execute on that machine. Scheduling policies can be classified as adaptive or non-adaptive based on whether or not they utilize information learned from the instantiation of processing times of previously-completed jobs in their future scheduling decisions. A novel aspect of our work lies in studying the benefit one can obtain through adaptivity, as we show that for all of our stochastic scheduling problems, adaptivity can only allow us to improve the expected value obtained by an optimal policy by at most a small constant factor. All of the problems we consider are at least NP-hard since they contain the deterministic 0/1 knapsack problem as a special case. We therefore seek to develop approximation algorithms: algorithms that run in polynomial time and compute a policy whose expected value is provably close to that of an optimal adaptive policy.
Author: M.A. Dempster
Publisher: Springer Science & Business Media
ISBN: 9400978014
Category : Mathematics
Languages : en
Pages : 418
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Book Description
This volume contains the proceedings of an Advanced Study and Re search Institute on Theoretical Approaches to Scheduling Problems. The Institute was held in Durham, England, from July 6 to July 17, 1981. It was attended by 91 participants from fifteen different countries. The format of the Institute was somewhat unusual. The first eight of the ten available days were devoted to an Advanced Study Insti tute, with lectures on the state of the art with respect to deter ministic and stochastic scheduling models and on the interface between these two approaches. The last two days were occupied by an Advanced Research Institute, where recent results and promising directions for future research, especially in the interface area, were discussed. Altogether, 37 lectures were delivered by 24 lecturers. They have all contributed to these proceedings, the first part of which deals with the Advanced Study Institute and the second part of which covers the Advanced Research Institute. Each part is preceded by an introduction, written by the editors. While confessing to a natural bias as organizers, we believe that the Institute has been a rewarding and enjoyable event for everyone concerned. We are very grateful to all those who have contributed to its realization.
Author: Jacob Healy Scott
Publisher:
ISBN:
Category :
Languages : en
Pages : 67
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Book Description
Motivated by problems in distributed computing, this thesis presents the first nontrivial polynomial time approximation algorithms for an important class of machine scheduling problems. We study the family of preemptive minimum makespan scheduling problems where jobs have stochastic processing requirements and provide the first approximation algorithms for these problems when machines have unrelated speeds. We show a series of algorithms that apply given increasingly general classes of precedence constraints on jobs. Letting n and m be, respectively, the number of jobs and machines in an instance, when jobs need an exponentially distributed amount of processing, we give: -- An O(log log min {m, n} )-approximation algorithm when jobs are independent; -- An 0 (log(n + m) log log min {m, n})-approximation algorithm when precedence constraints form disjoint chains; and, -- An O(log n log(n + m) log log min {m, n} )-approximation algorithm when precedence constraints form a directed forest. Very simple modifications allow our algorithms to apply to more general distributions, at the cost of slightly worse approximation ratios. Our O(log log n)-approximation algorithm for independent jobs holds when we allow restarting instead of preemption. Here jobs may switch machines, but lose all previous processing if they do so. We also consider problems in the framework of scheduling under uncertainty. This model considers jobs that require unit processing on machines with identical speeds. However, after processing a job to completion, a machine has an (unrelated) probability of failing and leaving the job uncompleted. This difficulty is offset by allowing multiple machines to process a job simultaneously. We prove that this model is equivalent to a slightly modified version of the family of problems described above and provide approximation algorithms for analogous problems with identical ratios.
Author: Dimitri P. Bertsekas
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Book Description
Author: Joseph Y-T. Leung
Publisher: CRC Press
ISBN: 0203489802
Category : Business & Economics
Languages : en
Pages : 1215
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Book Description
This handbook provides full coverage of the most recent and advanced topics in scheduling, assembling researchers from all relevant disciplines to facilitate new insights. Presented in six parts, these experts provides introductory material, complete with tutorials and algorithms, then examine classical scheduling problems. Part 3 explores scheduling models that originate in areas such as computer science, operations research. The following section examines scheduling problems that arise in real-time systems. Part 5 discusses stochastic scheduling and queueing networks, and the final section discusses a range of applications in a variety of areas, from airlines to hospitals.
Author: Daniel Bienstock
Publisher: Springer Science & Business Media
ISBN: 3540221131
Category : Computers
Languages : en
Pages : 453
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Book Description
This book constitutes the refereed proceedings of the 10th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2004, held in New York City, USA in June 2004. The 32 revised papers presented were carefully reviewed and selected from 109 submissions. Among the topics addressed are vehicle routing, network management, mixed-integer programming, computational complexity, game theory, supply chain management, stochastic optimization problems, production scheduling, graph computations, computational graph theory, separation algorithms, local search, linear optimization, integer programming, graph coloring, packing, combinatorial optimization, routing, flow algorithms, 0/1 polytopes, and polyhedra.
Author: Roberto Solis-Oba
Publisher: Springer Science & Business Media
ISBN: 3642291155
Category : Computers
Languages : en
Pages : 283
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Book Description
This book constitutes the thoroughly refereed post-proceedings of the 9th International Workshop on Approximation and Online Algorithms, WAOA 2011, held in Saarbrücken, Germany, in September 2011. The 21 papers presented were carefully reviewed and selected from 48 submissions. The volume also contains an extended abstract of the invited talk of Prof. Klaus Jansen. The Workshop on Approximation and Online Algorithms focuses on the design and analysis of algorithms for online and computationally hard problems. Both kinds of problems have a large number of applications in a wide variety of fields. Topics of interest for WAOA 2011 were: algorithmic game theory, approximation classes, coloring and partitioning, competitive analysis, computational finance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, packing and covering, paradigms for design and analysis of approximation and online algorithms, parameterized complexity, randomization techniques and scheduling problems.
Author: Harold Kushner
Publisher: Springer Science & Business Media
ISBN: 038721769X
Category : Mathematics
Languages : en
Pages : 485
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Book Description
This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.
Author: Josep Diaz
Publisher: Springer Science & Business Media
ISBN: 3540380442
Category : Computers
Languages : en
Pages : 532
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Book Description
This is the joint refereed proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and the 10th International Workshop on Randomization and Computation, RANDOM 2006. The book presents 44 carefully reviewed and revised full papers. Among the topics covered are design and analysis of approximation algorithms, hardness of approximation problems, small spaces and data streaming algorithms, embeddings and metric space methods, and more.
Author: Dorit Hochbaum
Publisher: Springer
ISBN: 3540484132
Category : Computers
Languages : en
Pages : 297
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Book Description
This book constitutes the refereed proceedings of the Third International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM'99, held jointly with the Second International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX'99, in Berkeley, California in August 1999. The volume presents 24 revised full papers selected from 44 submissions and four invited contributions. The papers present a wealth of new results and document the state-of-the-art in the areas covered by the workshop.
