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The maximum clique problem (MCP) is a classic graph optimization problem with many real-world applications.
Then the backbone network energy optimizing problem is transformed to the maximum clique problem (MCP).
In this study, our focus is on the weighted maximum clique problem, a highly challenging problem in graph theory.
For disk graphs, we consider two variations of the maximum clique problem, namely geometric clique and graphical clique.
We present a P system with replicated rewriting to solve the Maximum Clique Problem for a graph.
Here, we study two parallel implementations on SIMD computers of multiple restarts Hopfield networks for solving the maximum clique problem.
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This new algorithm (MMMvII) solves the problem of finding the maximum submatrices exactly, and is rendered much faster than MMM by expressing the problem as a series of maximum clique problems, and leveraging existing efficient techniques to solve them.
Therefore, MMMvII's significantly better measured performance compared to MMM (which we will show) implies that, in practice, the maximum clique problems generated by MMMvII do not actually exhibit the worst-case exponential behaviour.
Many existing algorithms convert the MCS problem into a maximum clique finding problem, by introducing an association graph (Hattori et al., 2003).
To serve the maximum number of devices according to their prioritization, the maximum weight clique problem is sequentially solved for layers (mathcal {L}_{delta } kappa), delta =1, cdots ) containing the vertices connected to the maximum weight clique chosen so far.
Given an undirected graph with positive weights on the vertices, the Maximum Weight Clique Problem (MWCP) consists in finding a clique with maximum total weight.
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