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Substituting the result of Lemma 3 in the inequality (21) gives the sufficient condition (18) to transform the maximum weight clique search to a maximum clique problem: □.
This section proposes reducing the complexity of finding the optimal solution to the maximum-delay reduction problem by deriving a sufficient condition to transform the maximum weight clique search to a maximum clique problem.
A sufficient condition to transform the maximum weight clique search to a maximum clique problem is the following: begin{array}{*{20}l} |M_{w}| leq w_{max}/Delta_{w}.
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Afterwards, the paper derives sufficient conditions for reducing the size of the graph and transforming the maximum weight clique search to a simpler maximum clique discovery problem.
The first algorithm is the optimal solution found by transforming the maximum lifetime scheduling problem to the Multicommodity Network Flow problem, and solved by AMPL-CPLEX [38], which is denoted as Optimal in our figures.
In both cases the shift introduced by the Fresnel rhomb transforms the maxima and minima in Fig. 4(b) into points at 50%% transmittance, therefore improving the accuracy at these wavelengths.
The second and third elements (a_{{x_{2} }}) and (a_{{x_{3} }}) transform the minimum and maximum change in mass defect with changing peak mass to a metric scale that can be represented in a k-d tree.
Therefore, we attempt to transform the above maximum problem with multiple variables into a single variable optimization problem.
Based on a Gaussian approximation of the amplitude of combined chips in the balancing procedure, together with the orthogonal property of the transform, the distribution of the maximum of the chips amplitude among N transformed orthogonal codes of length N is given by p N ( z ) ≈ N 2 2 π e - z 2 2 erf z 2 N 2 - 1. (16).
They transform the problem to a maximum flow problem so that it can be solved optimally in a centralized manner.
Obviously, the problem is transformed to the maximum dual problem.
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