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Our study shows that the SIN property is intrinsically related to topological centre problems.
We study the interrelationships between strong Arens irregularity and quotient strong Arens irregularity, revealing the complex nature of topological centre problems.
Our results indicate that Zt ⟨A⁎A⟩⁎)⋄ is indispensable for investigating properties of module maps over A⁎ and for understanding some asymmetry phenomena in topological centre problems as well as the interrelationships between different Arens irregularity properties.
It is well know that the optimal GW deployment can be formulated as a vertex k-centre problem.
However, achieving the optimal solution of a k-centre problem is highly complex due to its large solution space.
However, in our case, we only consider the case of p=1, i.e., the 1-centre problem.
Simulation results show that the proposed t-step substitution algorithm can significantly reduce the solution space of the k-centre problem by up to 80%.
A VNS-based heuristic using both a facility as well as a customer type neighbourhood structure is proposed to solve the p-centre problem in the continuous space.
A self-adaptive heuristic that incorporates a variable level of perturbation, a novel local search and a learning mechanism is proposed to solve the p-centre problem in the continuous space.
As a by-product of this research, we also report for the first time the optimal solution of the vertex p-centre problem for these TSP-Lib data sets.
Instead, we can use an approach to the vertex p-centres problem [15] to determine the representative of the top-k anchors.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com