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Scheduling on Unrelated Machines Under Tree-Like Precedence Constraints [chapter]

V. S. Anil Kumar, Madhav V. Marathe, Srinivasan Parthasarathy, Aravind Srinivasan
2005 Lecture Notes in Computer Science  
We present polylogarithmic approximations for the R|prec|Cmax and R|prec| j wjCj problems, when the precedence constraints are "treelike" -i.e., when the undirected graph underlying the precedences is  ...  We use the same lower bound of "congestion+dilation", as in other job shop scheduling approaches.  ...  Introduction The most general scheduling problem involves unrelated parallel machines and precedence constraints, i.e., we are given: (i) a set of n jobs with precedence constraints that induce a partial  ... 
doi:10.1007/11538462_13 fatcat:sefzkarc5vapxo3lwiy6jhlkma

Scheduling on Unrelated Machines under Tree-Like Precedence Constraints

V. S. Anil Kumar, Madhav V. Marathe, Srinivasan Parthasarathy, Aravind Srinivasan
2007 Algorithmica  
We present polylogarithmic approximations for the R|prec|Cmax and R|prec| j wjCj problems, when the precedence constraints are "treelike" -i.e., when the undirected graph underlying the precedences is  ...  We use the same lower bound of "congestion+dilation", as in other job shop scheduling approaches.  ...  Introduction The most general scheduling problem involves unrelated parallel machines and precedence constraints, i.e., we are given: (i) a set of n jobs with precedence constraints that induce a partial  ... 
doi:10.1007/s00453-007-9004-y fatcat:arjytxhswrbx3lfcn3mwztw5fu

Improved approximations for multiprocessor scheduling under uncertainty

Christopher Y. Crutchfield, Zoran Dzunic, Jeremy T. Fineman, David R. Karger, Jacob H. Scott
2008 Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures - SPAA '08  
We show that our algorithms for SUU apply to a standard problem in this setting, giving the first approximation algorithms for preemptive stochastic scheduling on unrelated machines.  ...  on machine i for a single timestep.  ...  JOBS WITH TREE-LIKE PRECEDENCE CONSTRAINTS We can obtain algorithms for tree-like precedence constraints by trivially applying techniques from [7] , as done in [10] .  ... 
doi:10.1145/1378533.1378579 dblp:conf/spaa/CrutchfieldDFKS08 fatcat:wmd5skayhvfphgnost7kz46gwq

Search on the enumeration tree in the multiprocessor job-shop problem

Lester Carballo, Alexander A. Lazarev, Nodari Vakhania, Frank Werner
2012 IFAC Proceedings Volumes  
We present an approach based on a two-stage filtration of the set of feasible solutions for the multiprocessor job-shop scheduling problem.  ...  On the first stage we use extensive dominance relations, whereas on the second stage we use lower bounds. We show that several lower bounds can efficiently be obtained and implemented.  ...  We would like to obtain a lower bound for an extension of σ h with operation o scheduled on machine Q ∈ M k , σ h o Q ∈ T .  ... 
doi:10.3182/20120523-3-ro-2023.00414 fatcat:pq7ti5cr2nhxrjvvmf2smnhjj4

Improved Approximations for Multiprocessor Scheduling Under Uncertainty [article]

Christopher Crutchfield, Zoran Dzunic, Jeremy T. Fineman, David R. Karger, Jacob Scott
2008 arXiv   pre-print
on machine i for a single timestep.  ...  In the SUU problem we are given n unit-length jobs and m machines, a directed acyclic graph G of precedence constraints among jobs, and unrelated failure probabilities q_ij for each job j when executed  ...  B JOBS WITH TREE-LIKE PRECEDENCE CONSTRAINTS We can obtain algorithms for tree-like precedence constraints by trivially applying techniques from [7] , as done in [11] .  ... 
arXiv:0802.2418v2 fatcat:dzsgv7bdrbgmblu65tthjcfddm

Approximation algorithms for multiprocessor scheduling under uncertainty

Guolong Lin, Rajmohan Rajaraman
2007 Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '07  
Also extensively studied is the the problem of preemptively scheduling jobs with precedence constraints on unrelated parallel machines [19, 27, 17] , the processing time of a job depends on the machine  ...  Two particular variants of scheduling closely related to our work is job shop scheduling [27] and the scheduling of unrelated machines under precendence constraints.  ...  Tree-like precedence constraints Our algorithm for tree-like precedence constraints uses techniques from [17] , who extend the work of [27] on scheduling unrelated parallel machines with chain precedence  ... 
doi:10.1145/1248377.1248383 dblp:conf/spaa/LinR07 fatcat:z3pistditfduhpbqzyzqlbedea

Approximation Algorithms for Multiprocessor Scheduling under Uncertainty

Guolong Lin, Rajmohan Rajaraman
2010 Theory of Computing Systems  
Also extensively studied is the the problem of preemptively scheduling jobs with precedence constraints on unrelated parallel machines [19, 27, 17] , the processing time of a job depends on the machine  ...  Two particular variants of scheduling closely related to our work is job shop scheduling [27] and the scheduling of unrelated machines under precendence constraints.  ...  Tree-like precedence constraints Our algorithm for tree-like precedence constraints uses techniques from [17] , who extend the work of [27] on scheduling unrelated parallel machines with chain precedence  ... 
doi:10.1007/s00224-010-9250-2 fatcat:p5cjlb4zkneqzmoqll5njp2cvq

Scheduling subject to resource constraints: classification and complexity

J. Blazewicz, J.K. Lenstra, A.H.G.Rinnooy Kan
1983 Discrete Applied Mathematics  
In deterministic sequencing and scheduling problems, jobs are to be processed on machines of limited capacity.  ...  A classification scheme for resource constraints is proposed and the computational complexity of the extended problem class is investigated in terms of this classification.  ...  -p3 = tree (tree-like precedence constraints):H has outdegree at most one for each vetex or indegree at most one for each vertex.  ... 
doi:10.1016/0166-218x(83)90012-4 fatcat:fn7w2z3wrnbzfnnqhieyb6embq

The mystical power of twoness: in memoriam Eugene L. Lawler

Jan Karel Lenstra
1998 Journal of Scheduling  
Lawler, one of the early investigators of combinatorial optimization and the architect of deterministic machine scheduling theory.  ...  After sketching his research career and examining the development of his interests, I describe some of his seminal results in scheduling theory and recall one of his contributions to scientific journalism  ...  I am grateful to Tom Liebling, who invited me to give the talk on which this paper is based, to Edmund Burke, who asked me to contribute to the first issue of the new Journal of Scheduling, and to Petra  ... 
doi:10.1002/(sici)1099-1425(199806)1:1<3::aid-jos1>3.3.co;2-2 fatcat:kauex7gxxnanrfknclrgztddu4

The mystical power of twoness: in memoriam Eugene L. Lawler

Jan Karel Lenstra
1998 Journal of Scheduling  
Lawler, one of the early investigators of combinatorial optimization and the architect of deterministic machine scheduling theory.  ...  After sketching his research career and examining the development of his interests, I describe some of his seminal results in scheduling theory and recall one of his contributions to scientific journalism  ...  I am grateful to Tom Liebling, who invited me to give the talk on which this paper is based, to Edmund Burke, who asked me to contribute to the first issue of the new Journal of Scheduling, and to Petra  ... 
doi:10.1002/(sici)1099-1425(199806)1:1<3::aid-jos1>3.0.co;2-b fatcat:dbbwgjjgdzgarpbmvxgmpq3qvy

Page 1662 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
for tree-like precedence constraints [J.  ...  In this paper several scheduling problems are considered for the case of series-parallel precedence constraints.  ... 

Analyzing Branch-and-Bound Algorithms for the Multiprocessor Scheduling Problem [article]

Thomas Lively, William Long, Artidoro Pagnoni
2019 arXiv   pre-print
We find that in fact Fujita's method does not offer any improvement over the Fernandez bound on our data set.  ...  The Multiprocessor Scheduling Problem (MSP) is an NP-Complete problem with significant applications in computer and operations systems.  ...  Note that these quantities are completely determined from the graph of precedence constraints and do not depend on the number of machines.  ... 
arXiv:1901.07070v1 fatcat:tmyt2knomzg6bakrsovi2gr6yu

Scheduling Integrated Circuit Assembly Operations on Die Bonder

W. L. Pearn, S. H. Chung, C. M. Lai
2007 IEEE transactions on electronics packaging manufacturing (Print)  
Furthermore, the job processing time depends on the product type, and the machine setup time is sequentially dependent on the orders of jobs processed.  ...  Therefore, the ICASP is more difficult to solve than the classical parallel machine scheduling problem.  ...  However, the precedence relations studied in these papers can be presented by graphs in tree-types: in-tree type precedence (each job has at most one successor), out-tree type precedence (each job has  ... 
doi:10.1109/tepm.2007.899091 fatcat:jjrrlimwr5h4dcpltporfkptlu

A review of scheduling problem and resolution methods in flexible flow shop

Tian-Soon Lee, Ying-Tai Loong
2019 International Journal of Industrial Engineering Computations  
This review paper gives a comprehensive exploration review on the FFS scheduling problem and guides the reader by considering and understanding different environmental assumptions, system constraints and  ...  This paper gives a comprehensive guide for the reader with respect to future research work on the FFS scheduling problem.  ...  Acknowledgment The authors would like to thank the reviewers for their constructive comments and the Ministry of Higher  ... 
doi:10.5267/j.ijiec.2018.4.001 fatcat:kiq2jjjsmzgtpoaudrq4qc7ndi

LEARNING-BASED METAHEURISTIC FOR SCHEDULING UNRELATED PARALLEL MACHINES WITH UNCERTAIN SETUP TIMES

Chen-Yang Cheng, Pourya Pourhejazy, Kuo-Ching Ying, Shu-Fen Li, Chieh-Wen Chang
2020 IEEE Access  
The extant scheduling predominantly relies on simplistic methods, like the average value obtained from historical data, to estimate setup times.  ...  INDEX TERMS Scheduling, unrelated parallel machines, setup times, random-forest, metaheuristic.  ...  This situation is particularly prevalent in the Unrelated Parallel Machines Scheduling Problem (UPMSP).  ... 
doi:10.1109/access.2020.2988274 fatcat:hx3umfupgvc2ldw3kbwdpxris4
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