Approximation schemes for covering and scheduling in related machines

Author(s):  
Yossi Azar ◽  
Leah Epstein
2010 ◽  
Vol 21 (01) ◽  
pp. 27-49
Author(s):  
KLAUS JANSEN ◽  
ROBERTO SOLIS-OBA

We study the problem of scheduling jobs with precedence constraints and present two polynomial time approximation schemes for it. The first one is for the case when the machines are identical and the precedence graph partitions the jobs into groups of fixed size. As an interesting particular case, this yields a polynomial time approximation scheme for scheduling jobs with chain or tree precedence constraints on identical machines, when each chain or tree is of constant size. The second approximation scheme is for scheduling jobs with arbitrarily long chain precedence constraints on uniformly related machines when the number of machines is fixed.


Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3085
Author(s):  
Konstantin Osintsev ◽  
Seregei Aliukov ◽  
Alexander Shishkov

The problem of increasing the reliability of wind turbines exists in the development of new offshore oil and natural gas fields. Reducing emergency situations is necessary due to the autonomous operation of drilling rigs and bulk seaports in the subarctic and Arctic climate. The relevance of the topic is linked with the development of a methodology for theoretical and practical studies of gas dynamics when gas flows in a pipe, based on a mathematical model using new mathematical methods for calculation of excess speeds in case of wind gusts. Problems in the operation of offshore wind turbines arise with storm gusts of wind, which is comparable to the wave movement of the gas flow. Thus, the scientific problem of increasing the reliability of wind turbines in conditions of strong wind gusts is solved. The authors indicate a gross error in the calculations when approximating through the use of the Fourier series. The obtained results will allow us to solve one of the essential problems of modeling at this stage of its development, namely: to reduce the calculation time and the adequacy of the model built for similar installations and devices. Experimental studies of gas-dynamic flows are carried out on the example of a physical model of a wind turbine. In addition, a computer simulation of the gas-dynamic flow process was carried out. The use of new approximation schemes in processing the results of experiments and computer simulation can reduce the calculation error by 1.2 percent.


Author(s):  
Biswaroop Maiti ◽  
Rajmohan Rajaraman ◽  
David Stalfa ◽  
Zoya Svitkina ◽  
Aravindan Vijayaraghavan

2021 ◽  
Vol 434 ◽  
pp. 110234
Author(s):  
Gordey S. Goyman ◽  
Vladimir V. Shashkin

2019 ◽  
Vol 66 (4) ◽  
pp. 1-40
Author(s):  
Anna Adamaszek ◽  
Sariel Har-Peled ◽  
Andreas Wiese

2010 ◽  
Vol 57 (2) ◽  
pp. 1-32 ◽  
Author(s):  
Amit Kumar ◽  
Yogish Sabharwal ◽  
Sandeep Sen

2000 ◽  
Vol 35 (1) ◽  
pp. 108-121 ◽  
Author(s):  
Piotr Berman ◽  
Moses Charikar ◽  
Marek Karpinski

2016 ◽  
Vol 254 (1) ◽  
pp. 1600166 ◽  
Author(s):  
Jörg Bünemann ◽  
Thorben Linneweber ◽  
Florian Gebhard

Sign in / Sign up

Export Citation Format

Share Document