By Avella P., Boccia M., Sforza A.
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Additional info for A Branch-and-Cut Algorithm for the Median-Path Problem
Carter 4 Analysis of the Results In the experiments performed in this study, we set the resolution of the clustering as and the threshold for outlier detection as We required only one algorithm run for each data set to provide the presented results. 5GHz, with memory of 256MB. Firstly, the clustering was performed on all the synthetic data sets described in the previous section (SD1 to SD9). The correct clustering was achieved for all of them, meaning that the correct assignment of individuals to clusters was found.
Since there are fundamental cycles of size at most and fundamental cuts of size at most updating the fundamental cut and cycle structures after the application of an edge swap requires O(mn). Doing this for each branch of the tree and for each chord in the fundamental cut induced by the branch, leads to an total complexity. It is worth pointing out that computational experiments show larger speedups in the average running times (with respect to the basic implementation) than those suggested by the worst-case analysis.
3 fraction of the branches, where 21 is an arbitrary sampling Metaheuristics To go beyond the scope of local search and try to escape from local minima, we have implemented and tested two well-known metaheuristics: variable neighbourhood search (VNS)  and tabu search (TS) . 1 Variable Neighbourhood Search In VNS one attempts to escape from a local minimum by choosing another random starting point in increasingly larger neighbourhoods of If the cost of the local minimum obtained by applying the local search from is smaller than the cost of then becomes the new best local minimum and the neighbourhood size is reset to its minimal value.