Download or read book Approximation Algorithms for Job Scheduling with Block Type Conflict Graphs written by Hanna Furmanczyk and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model.The presented model stems from a well-established line of research combining scheduling theory with methods relevant to graph coloring. Recently, cluster graphs and their extensions like block graphs were given additional attention. We complement hardness results provided by other researchers for block graphs by providing approximation algorithms. In particular, we provide a 2-approximation algorithm for P|G = block graph|Cmax and a PTAS for the case when the jobs are unit time in addition. In the case of uniform machines, we analyze two cases. The first one is when the number of blocks is bounded, i.e. Q|G = k-block graph|Cmax. For this case, we provide a PTAS, improving upon results presented by D. Page and R. Solis-Oba. The improvement is two-fold: we allow richer graph structure, and we allow the number of machine speeds to be part of the input. Due to strong NP-hardness of Q|G = 2-clique graph|Cmax, the result establishes the approximation status of Q|G = k-block graph|Cmax. The PTAS might be of independent interest because the problem is tightly related to the NUMERICAL k-DIMENSIONAL MATCHING WITH TARGET SUMS problem. The second case that we analyze is when the number of blocks is arbitrary, but the number of cut-vertices is bounded and jobs are of unit time. In this case, we present an exact algorithm. In addition, we present an FPTAS for graphs with bounded treewidth and a bounded number of unrelated machines.

Download or read book Handbook of Scheduling written by Joseph Y-T. Leung and published by CRC Press. This book was released on 2004-04-27 with total page 1215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Combinatorial Optimization and Applications written by Ding-Zhu Du and published by Springer Nature. This book was released on 2021-12-10 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2021, which took place in Tianjin, China, during December 17-19, 2021. The 55 papers presented in this volume were carefully reviewed and selected from 122 submissions. They deal with combinatorial optimization and its applications in general, focusing on algorithms design, theoretical and experimental analysis, and applied research of general algorithmic interest.

Download or read book Approximation Algorithms for Time Constrained Scheduling written by Klaus Jansen and published by . This book was released on 1995 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In this paper we consider the following time constrained scheduling problem. Given a set of jobs J with execution times e(j)[belonging to] (0,1] and an undirected graph G = (J, E), we consider the problem to find a schedule for the jobs such that adjacent jobs (j, j') [belonging to] E are assigned to different machines and that the total execution time for each machine is at most 1. The goal is to find a minimum number of machines to execute all jobs under this time constraint. This scheduling problem is a natural generalization of the classical bin packing problem. We propose and analyse several approximation algorithms with constant absolute worst case ratio for graphs that can be colored in polynomial time."

Download or read book Scheduling Algorithms written by Peter Brucker and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains algorithms for classical and complex scheduling problems, new results on scheduling problems arising in flexible manufacturing, and an extensive overview of the area of scheduling. The methods used to solve these problems include: linear programming, dynamic programming, branch-and-bound algorithms, and local search heuristics. In the third edition of the book the complexity status of the different classes of scheduling problems has been updated. New polynomial algorithms for single machine problems with release times and constant processing times have been added.

Download or read book An Analysis of Scheduling Algorithms in Multiprocessor Computing Systems written by Nai-Fung Chen and published by . This book was released on 1975 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation Algorithms for Multiprocessor Task Scheduling written by Antonio Miranda-Garcia and published by . This book was released on 1998 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Tight Approximation Algorithms for Scheduling with Fixed Jobs and Non availability written by Florian Diedrich and published by . This book was released on 2009 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation Algorithms Heuristics for Job Shop Scheduling written by Dan Dan Lin and published by . This book was released on 1998 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation Algorithms for Scheduling Parallel Jobs Breaking the Approximation Ratio of 2 written by Klaus Jansen and published by . This book was released on 2008 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation Algorithms for Scheduling Problems with Multi type Contentions and Related Problems written by Zhenming Chen and published by . This book was released on 2007 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scheduling problem is a fundamental and versatile problem in theoretical computer science. It has been extensively studied in many different variations. Most of existing scheduling models only deal with one type of resources, i.e., the machines. However, in many applications, besides the machines, there are other types of critical resources that the jobs may compete for. Different types of resources cause different types of contentions, and the contentions could interfere with each other, which complicate the problem dramatically. In this dissertation, we study the scheduling problems with multi-type contentions and several related problems.

Download or read book Approximation Algorithms for Scheduling and Fair Allocations written by Yihao Zhang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we will have discussions on two main topics, max-min allocation and schedulingjobs with precedent constraints on machines with communication delays. New approximation algorithms are given in Chapter 2, 4 and 5, where linear programming plays a fairly important role on algorithm designs, while Chapter 3 contains partial results on the general max-min allocation. The Santa Claus problem is also known as the restricted max-min fair allocation. In this problem, Santa Claus has a set of gifts, and he wants to distribute them among a set of children so that the least happy child is made as happy as possible. Here, the value that a child i has for a present j is of the form pij [is an element of] {0, pj}. Based on a modification of Haxell's hypergraph matching argument, a polynomial time algorithm by Annamalai et al. gives a 12.33-approximation. In joint work with Sami Davies and Thomas Rothvoss, a matroid version of the Santa Claus problem is introduced. The algorithm is based on Haxell's augmenting tree, but with the introduction of the matroid structure. Our result can then be used as a blackbox to obtain a (4 + [epsilon])-approximation for Santa Claus, comparing against a natural, compact LP. A recent work of Cheng and Mao [CM19] also gets the factor (4 + [epsilon]). On the second half, we first consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays. In this setting, denoted by P | prec, c | Cmax, if two dependent jobs are scheduled on different machines, then at least c units of time must pass between their executions. Despite its relevance to many applications, the best known approximation ratio was O(c), whereas Graham's greedy list scheduling algorithm already gives a (c + 1)-approximation in that setting. An outstanding open problem in the top-10 list by Schuurman and Woeginger and its recent update by Bansal asks whether there exists a constant-factor approximation algorithm. In joint work with Sami Davies, Janardhan Kulkarni, Thomas Rothvoss and Jakub Tarnawski, we give a polynomial-time O(log c · log m)-approximation algorithm for this problem, where m is the number of machines and c is the communication delay. Our approach is based on a Sherali-Adams lift of a linear programming relaxation and a randomized clustering of the semimetric space induced by this lift. Finally, a more general version of this problem is considered in Chapter 5, to minimize the weighted sum of completion times on related machines, denoted by Q | prec, c | wjCj . Our main result is an O(log4 n)-approximation algorithm for the problem. As a byproduct of our result, we also obtain an O(log3 n)-approximation algorithm for the problem of minimizing makespan Q | prec, c | Cmax, which improves upon the O(log5 n/ log log n)-approximation algorithm due to a recent work of Maiti et al. [MRS+20].

Download or read book Approximation Algorithms for Stochastic Scheduling on Unrelated Machines written by Jacob Healy Scott and published by . This book was released on 2008 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Combinatorial Optimization and Applications written by Ding-Zhu Du and published by Springer. This book was released on 2021-12-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2021, which took place in Tianjin, China, during December 17-19, 2021. The 55 papers presented in this volume were carefully reviewed and selected from 122 submissions. They deal with combinatorial optimization and its applications in general, focusing on algorithms design, theoretical and experimental analysis, and applied research of general algorithmic interest.

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.

Download or read book Scheduling Theory Single Stage Systems written by V. Tanaev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scheduling theory is an important branch of operations research. Problems studied within the framework of that theory have numerous applications in various fields of human activity. As an independent discipline scheduling theory appeared in the middle of the fifties, and has attracted the attention of researchers in many countries. In the Soviet Union, research in this direction has been mainly related to production scheduling, especially to the development of automated systems for production control. In 1975 Nauka ("Science") Publishers, Moscow, issued two books providing systematic descriptions of scheduling theory. The first one was the Russian translation of the classical book Theory of Scheduling by American mathematicians R. W. Conway, W. L. Maxwell and L. W. Miller. The other one was the book Introduction to Scheduling Theory by Soviet mathematicians V. S. Tanaev and V. V. Shkurba. These books well complement each other. Both. books well represent major results known by that time, contain an exhaustive bibliography on the subject. Thus, the books, as well as the Russian translation of Computer and Job-Shop Scheduling Theory edited by E. G. Coffman, Jr., (Nauka, 1984) have contributed to the development of scheduling theory in the Soviet Union. Many different models, the large number of new results make it difficult for the researchers who work in related fields to follow the fast development of scheduling theory and to master new methods and approaches quickly.

Download or read book Ant Colony Optimization written by Marco Dorigo and published by MIT Press. This book was released on 2004-06-04 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the rapidly growing field of ant colony optimization that describes theoretical findings, the major algorithms, and current applications. The complex social behaviors of ants have been much studied by science, and computer scientists are now finding that these behavior patterns can provide models for solving difficult combinatorial optimization problems. The attempt to develop algorithms inspired by one aspect of ant behavior, the ability to find what computer scientists would call shortest paths, has become the field of ant colony optimization (ACO), the most successful and widely recognized algorithmic technique based on ant behavior. This book presents an overview of this rapidly growing field, from its theoretical inception to practical applications, including descriptions of many available ACO algorithms and their uses. The book first describes the translation of observed ant behavior into working optimization algorithms. The ant colony metaheuristic is then introduced and viewed in the general context of combinatorial optimization. This is followed by a detailed description and guide to all major ACO algorithms and a report on current theoretical findings. The book surveys ACO applications now in use, including routing, assignment, scheduling, subset, machine learning, and bioinformatics problems. AntNet, an ACO algorithm designed for the network routing problem, is described in detail. The authors conclude by summarizing the progress in the field and outlining future research directions. Each chapter ends with bibliographic material, bullet points setting out important ideas covered in the chapter, and exercises. Ant Colony Optimization will be of interest to academic and industry researchers, graduate students, and practitioners who wish to learn how to implement ACO algorithms.