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A polynomial algorithm for an open shop problem with unit processing times and tree constraints

H. Bräsel, D. Kluge, F. Werner
1995 Discrete Applied Mathematics  
In this paper we consider the open shop problem with unit processing times and tree constraints (outtree) between the jobs. The complexity of this problem was open.  ...  Each subproblem can be solved on the base of an algorithm for the corresponding open shop problem without tree constraints.  ...  Assume that the jobs 2,3 and 4 have been For unit time open shop problems, there exist several polynomial time algorithms. Gonzales [S] and Tanaev et al.  ... 
doi:10.1016/0166-218x(93)e0156-s fatcat:34dnlf563nbpxftgcm5al3nqp4

Polynomial time algorithms for special open shop problems with precedence constraints and unit processing times

Heidemarie Bräsel, Dagmar Kluge, Frank Werner
1996 Reserche operationelle  
CONCLUDING REMARKS In this paper we gave polynonüal time algorithms for two 2-machine open shop problems with unit processing times and different types of precedence constraints.  ...  THE PROBLEM O2\ Pij = 1, prec|C max We consider the open shop problem with n jobs, 2 machines and unit processing times.  ... 
doi:10.1051/ro/1996300100651 fatcat:ivphk5r4bjak5kjeidt3cttrbm

Page 2541 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
[Werner, Frank] (D-MAG; Magdeburg) A polynomial algorithm for an open shop problem with unit processing times and tree constraints. (English summary) Discrete Appl. Math. 59 (1995), no. 1, 11-21.  ...  Summary: “In this paper we consider the open shop problem with unit processing times and tree constraints (outtree) between the jobs. The complexity of this problem was open.  ... 

Page 2000 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
An O(n*m*") algorithm is presented for a unit time open shop problem with n jobs, m machines, release times, and mean flow time as objective function. This algorithm is based on dynamic programming.  ...  The scheduling problem of minimizing the number of tardy jobs with precedence constraints and unit processing times on a single machine is considered.  ... 

Page 1477 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
We also investigate the problems of scheduling on parallel ma- chines with precedence constraints and unit processing times, and two variants of the latter problem with unit communication delays; for these  ...  We further show APX- hardness for scheduling in flow shops, job shops, and open shops.  ... 

Page 2696 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
Unit time open shop problems with release times to minimize total completion time were unsolved up to now for both allowed and forbidden delay times.  ...  Summary: “We consider open shop problems with unit processing times in which n jobs have to be processed on m machines. The order in which a given job is processed on the machines is not fixed.  ... 

Page 1342 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
special open shop problems with precedence constraints and unit processing times.  ...  The complexity of the open shop problem with unit processing times and intree constraints among the jobs was open up to now if the sum of completion times of the jobs has to be minimized.  ... 

Literature Review of Open Shop Scheduling Problems

Ellur Anand, Ramasamy Panneerselvam
2015 Intelligent Information Management  
This paper discusses review of literature of open shop scheduling problems.  ...  Directions for future research are discussed in the end. 1 2 , n J J J and a set M which consists of m machines { } 1 2  ...  Acknowledgements The authors thank the anonymous referees for their constructive suggestions, which have improved the paper. References  ... 
doi:10.4236/iim.2015.71004 fatcat:shukynonjrfaleqiousjru3ari

Page 2103 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
time approximation algorithm with ratio 5 and a polynomial time approximation scheme for optimal single-batch policies, and an O(kn*) time approximation algorithm with ratio 4 for optimal k-batch policies  ...  For the two-machine case, an improved heuristic guarantees a tight worst-case ratio of 3/2. For some two-machine problems with special setup and processing times, polynomial algorithms are presented.  ... 

Page 7441 of Mathematical Reviews Vol. , Issue 90M [page]

1990 Mathematical Reviews  
Summary: “Consider a set of n tasks with a tree-structured prece- dence relation and execution time of | or 3 units. We give an O(n?  ...  The main result obtained is an O(n) algorithm for the three-machine problem with a dominated machine.” 90m:90153 90B35 Aksénov, V. A.  ... 

Feasible edge colorings of trees with cardinality constraints

D. de Werra, A. Hertz, D. Kobler, N.V.R. Mahadev
2000 Discrete Mathematics  
We show that for trees with ÿxed maximum degree, one can ÿnd in polynomial time an edge k-coloring where for i = 1; : : : ; k the number of edges of color i is exactly a given number hi, and each edge  ...  This problem is NP-complete for general bipartite multigraphs. Applications to open shop problems with costs for using colors are described.  ...  Note that if there are no cardinality constraints, (G; ; H ) is solvable in polynomial time for trees (with the algorithm in [17] ).  ... 
doi:10.1016/s0012-365x(00)00006-6 fatcat:qyz6i4hi25fjtoskb4w4tq5b2m

Improved results for data migration and open shop scheduling

Rajiv Gandhi, Magnús M. Halldórsson, Guy Kortsarz, Hadas Shachnai
2006 ACM Transactions on Algorithms  
Queyranne and Sviridenko [18] gave a 5.83-approximation algorithm for the nonpreemptive version of the open shop problem.  ...  They state as an obvious open question whether there exists an algorithm for open shop scheduling that gives a performance guarantee better than 5.83.  ...  Acknowledgments: The first author would like to thank Yoo-Ah Kim for introducing to the author the problem of data migration, and Samir Khuller, Yoo-Ah Kim, Aravind Srinivasan, Chaitanya Swamy for useful  ... 
doi:10.1145/1125994.1126001 fatcat:p7zcya2ibzegnhpnyx77ordiim

Improved Results for Data Migration and Open Shop Scheduling [chapter]

Rajiv Gandhi, Magnús M. Halldórsson, Guy Kortsarz, Hadas Shachnai
2004 Lecture Notes in Computer Science  
Queyranne and Sviridenko [18] gave a 5.83-approximation algorithm for the nonpreemptive version of the open shop problem.  ...  They state as an obvious open question whether there exists an algorithm for open shop scheduling that gives a performance guarantee better than 5.83.  ...  Acknowledgments: The first author would like to thank Yoo-Ah Kim for introducing to the author the problem of data migration, and Samir Khuller, Yoo-Ah Kim, Aravind Srinivasan, Chaitanya Swamy for useful  ... 
doi:10.1007/978-3-540-27836-8_56 fatcat:qa2uyv6uvrcvja3bsnah6pxotu

Page 2794 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
Summary: “This paper develops polynomial time algorithms to solve the m machine flow shop and open shop makespan problems with a critical machine (that processes all jobs) and at most two Operations per  ...  This problem is shown to be strongly NP-hard, even for the case of unit processing time and zero set-up time.  ... 

Open shop problem with zero-one time operations and integer release date/deadline intervals

Marek Kubale
1997 Discrete Applied Mathematics  
We study the problem of constructing a minimum makespan schedule for the n-job m-machine open shop with zero-one time operations and integer release dates and deadlines.  ...  Two polynomial-time algorithms are given for the following special cases: (1) all possible mn operations have unit execution time, and (2) at most m + n operations have unit execution time.  ...  What is important, almost all problems with identical processing times are polynomially solvable. The only UET open-shop problems that are known to be NP-hard are some no-wait models of scheduling.  ... 
doi:10.1016/s0166-218x(96)00126-6 fatcat:2xikmrlvtneuplawr5ewljmege
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