scholarly journals Approximation Schemes for Subset Sum Ratio Problems

2020 ◽  
pp. 96-107
Author(s):  
Nikolaos Melissinos ◽  
Aris Pagourtzis ◽  
Theofilos Triommatis
Keyword(s):  
Approximation Schemes ◽  
Subset Sum

Parallel approximation schemes for Subset Sum and Knapsack problems

1987 ◽  
Vol 24 (4) ◽  
pp. 417-432 ◽  
Author(s):  
Joseph G. Peters ◽  
Larry Rudolph
Keyword(s):  
Knapsack Problems ◽  
Approximation Schemes ◽  
Subset Sum ◽  
Parallel Approximation

scholarly journals Trivial geometric heuristic for subset sum problem

2017 ◽  
Author(s):  
R U
Keyword(s):  
Greedy Algorithm ◽  
Dimensional Space ◽  
Approximate Solutions ◽  
Exact Algorithms ◽  
Approximation Schemes ◽  
Brute Force ◽  
Discrete Structure ◽  
Subset Sum Problem ◽  
Subset Sum ◽  
Hyper Plane

All exact algorithms for solving subset sum problem (SUBSET\_SUM) are exponential (brute force, branch and bound search, dynamic programming which is pseudo-polynomial). To find the approximate solutions both a classical greedy algorithm and its improved variety, and different approximation schemes are used.This paper is an attempt to build another greedy algorithm by transferring representation of analytic geometry to such an object of discrete structure as a set. Set of size $n$ is identified with $n$-dimensional space with Euclidean metric, the subset-sum is identified with (hyper)plane.

On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

2020 ◽  
Vol 25 (4) ◽  
pp. 10-15
Author(s):  
Alexander Nikolaevich Rybalov
Keyword(s):  
Linear Group ◽  
Modular Group ◽  
Special Linear Group ◽  
Second Order ◽  
Integer Matrix ◽  
Subset Sum ◽  
Algorithmic Problems ◽  
Almost All ◽  
Subset Sum Problems ◽  
Generic Complexity

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.

scholarly journals Improvement Dependability of Offshore Horizontal-Axis Wind Turbines by Applying New Mathematical Methods for Calculation the Excess Speed in Case of Wind Gusts

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3085
Author(s):  
Konstantin Osintsev ◽  
Seregei Aliukov ◽  
Alexander Shishkov
Keyword(s):  
Computer Simulation ◽  
Wind Turbines ◽  
Experimental Studies ◽  
Offshore Wind ◽  
Approximation Schemes ◽  
Calculation Error ◽  
Strong Wind ◽  
Mathematical Methods ◽  
Wind Gusts ◽  
Gas Dynamic

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.

Horizontal approximation schemes for the staggered reduced latitude-longitude grid

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