Facility Location with Tree Topology and Radial Distance Constraints

Algorithm 1

Proposed heuristics.

	Data: input matrices and and input graph .
	Result: a feasible solution for .
	for each do
	Step 1:;
	Set , ;
	, ;
	Remove all neighbors of from W;
	Find the minimum spanning tree formed with nodes in S using the Kruskal algorithm;
	Assign each user to its nearest facility in S and compute the objective function value of ;
	Save the current solution found if its objective function value is less than the best found so far;
	Step 2:;
	while ( is not empty) do
	Let be the vertex with minimum degree in ;
	, ;
	Remove all neighbors of from W;
	Find the minimum spanning tree formed with nodes in S using the Kruskal algorithm;
	Assign each user to its nearest facility in S and compute the objective function value of ;
	Save the current solution found if its objective function value is less than the best found so far;
	Return the best solution found and its objective function value;