We consider the facility location problem of locating a set $$X_p$$ X p of p facilities (resources) on a network (or a graph) such that the subnetwork (or subgraph) induced by the selected set $$X_p$$ X p is connected. Two problems on a block graph G are proposed: one problem is to minimizes the sum of its weighted distances from all vertices of G to $$X_p$$ X p , another problem is to minimize the maximum distance from each vertex that is not in $$X_p$$ X p to $$X_p$$ X p and, at the same time, to minimize the sum of its distances from all vertices of G to $$X_p$$ X p . We prove that the first problem is linearly solvable on block graphs with unit edge length. For the second problem, it is shown that the set of Pareto-optimal solutions of the two criteria has cardinality not greater than n, and can be obtained in $$O(n^2)$$ O ( n 2 ) time, where n is the number of vertices of the block graph G.
Journal of Combinatorial Optimization – Springer Journals
Published: Jul 13, 2016
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