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The key feature of the problem at hand is that it does not possess optimal substructure, that is, it cannot be solved (optimally) by an efficient combination of optimal solutions of its smaller subproblems.
They can therefore be solved optimally by dual optimisation.
Then Problem (40) can be solved optimally by directly applying Algorithm 1 with the modified Problem P1 to check the feasibility.
By constructing a novel delay graph, the problem can be solved optimally by employing the M node-disjoint paths algorithm under FDMA channel model.
To handle these cases, we convert the problem to an MaxSAT problem, which can be solved optimally by an MaxSAT solver.
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In that case, problem (61) is solved optimally by bracketing method[30, 31].
To detect the tag, it is sufficient to analyze the presence of the harmonic sinusoidal components at 2f 1 and 2f 2. The detection of sinusoidal signals in noise with a random unknown phase is a well-known problem in detection theory which is solved optimally by employing matched filter-envelope detectors (MFEDs) (also called quadrature matched filter) [36].
Thus, it can be solved optimally and efficiently by using the water filling algorithm, which is proposed for the multi-user transmit optimization for broadcast channels.
If host switching events are not considered then the problem can be solved optimally in polynomial time by a simple greedy algorithm.
However, this combinatorial optimization problem can be solved optimally in a reasonable CPU only when very small instances are considered.
Shortest path problems on single-source DAGs can be solved optimally in polynomial time [11].
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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