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We present the design and analysis of a parallel approximation algorithm for the problem of scheduling jobs on parallel identical machines to minimize makespan.
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Cell conductivity is calculated from a parallel resistor approximation depending on the gas phase distribution.
The analytical approach based on a single process execution model is extended to a multiprogramming environment using a queuing network model, as well as to a simpler approach using a "parallel processing" approximation.
Simple theory based on a parallel wire approximation to rectangular inductors is developed to allow the variation of the coupling coefficient with angle and radius to be estimated, and hence determine the location of the pivot.
For strictly diagonally dominant linear systems, one parallel approximation algorithm has been proposed [34].
The design of the parallel approximation algorithm is based on the best existing polynomial-time approximation scheme (PTAS) for the problem.
Here the propagation of Transverse Magnetic waves at the interface between a nonlinear dielectric material and a photonic hypercrystal is studied and the corresponding dispersion relation is derived using the uniaxial parallel approximation.
The results show that our proposed parallel approximation algorithm achieves significant speedup with respect to both the sequential PTAS and the CPLEX-based solver that solves the mixed integer program formulation of the problem.
To the best of our knowledge, this is the first practical parallel approximation algorithm for the minimum makespan scheduling problem that maintains the approximation guarantees of the sequential PTAS and it is specifically designed for execution on shared-memory parallel machines.
The algorithms that provide near optimal performance are not feasible to use in practice due to their huge execution time requirements, thus underscoring the importance of developing efficient parallel approximation algorithms with near-optimal performance guarantees that are suitable for execution on current parallel systems, such as multi-core systems.
To accelerate the computation process of rough set approximations, this paper first presents the boolean matrix representation of the lower and upper approximations in the composite information system, then designs a parallel method for computing approximations based on matrix, and implements it on Multi-GPU.
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