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The first subproblem is translated into a weighted sum rate maximization problem that can be efficiently solved for different channel models.
In their paper "Throughput-optimal scheduling with low average delay for cellular broadcast systems," the first subproblem is translated into a weighted sum rate maximization problem that can be efficiently solved for different channel models.
In our paper we further investigate the topic and point out several problems that need to be efficiently solved for the Internet of Things to work on large scale numbers.
The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions.
The two key differences between the methods in [31] and [32] and the LRSMs are (1) the LRSMs are able to adequately handle multiple features, drawn from different feature spaces, and (2) the least squares loss function is employed instead of hinge loss, resulting into formulation (4) which can be efficiently solved for large-scale data.
After discarding multireads, [ 18] formulates IE for a given set of isoforms as a convex quadratic program (QP) that can be efficiently solved for each gene locus.
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Extensive numerical experiments based on realistic Asia Europe Oceania shipping operations show that the proposed model can be efficiently solved by CPLEX for real-case problems.
For the W-subproblem, it is also a linear least square problem, which can be efficiently solved [33], and for the W ′-subproblem, it is a standard l 2,1-norm optimization problem, which can be solved by group shrinkage operator [42].
The integrated decision problem is a nonlinear mixed integer model which cannot be efficiently solved using classical methods for large problems.
The motivation for using tree-structure decompositions of graphs, such as tree-decompositions or clique-width k-expression trees, stems mainly from the fact that the independent set problem, for example, can be efficiently solved by applying dynamic programming on such a representation (tree structure) [20,24].
Second, they arise in contexts in which we are interested in solving not only isolated instances of the problem in question, but rather in developing methods which allow it to be efficiently solved on a mass scale – i.e. for all instances in which we might be practically concerned.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com