Instances used in the paper: Edge downgrades in the Maximal Covering Location Problem

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Instances used in the paper: Edge downgrades in the Maximal Covering Location Problem --------------- Data structure: num nodes num edges RatleastOne RatLeast5Per RatLeast10Per sum c_e*u_e vector of nodes demands adjacency matrix vector of downgrading bounds vector of downgrading costs -------------- Data generation: The nodes were given by points whose coordinates followed a uniform distribution over [0,30]. We then built the complete graph, where the length of the edges is the Euclidean distance between the nodes rounded to two decimal places. These instances are called "graph" followed by n (the number of vertices); for example, "graph50" is a complete graph with 50 nodes and 1225 edges. The selection of parameters is outlined as follows. The number of facilities denoted as p was determined in proportion to the number of vertices, specifically, $p\in \{n/30, n/20, n/10\}$. The weights or demands assigned to nodes, denoted as $w_i$ for $i\in V$, were uniformly randomly generated integers from 1 to 100. We tested three different coverage radii, R, such that each node can cover at least one node, at least 5% of the number of nodes, and at least 10\% of the number of nodes, respectively. Downgrading costs, $c_e,$ for $e\in E,$ were uniformly randomly generated between 1 and 3 with two decimal places. The upper bounds $u_e$, for $e\in E,$ were uniformly randomly generated from $(0.5\ell_e, 1.5\ell_e),$ for $e\in E$ with two decimal places. Finally, the budget B was computed as follows. We calculated the maximum required budget for downgrading all the edges, $B_{max}=\sum_{e\in E} u_ec_e,$ selected $B_{per}\in \{0.1, 0.05, 0.025\},$ and computed B as: $B=\frac{B_{max}\cdot B_{per} \cdot p \cdot (p-1)}{n (n-1)} $ rounded to two decimal places. For each combination of parameters, five instances were generated with the same procedure, varying only the random seed for the generator.

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