# Algorithms for connected p-centdian problem on block graphs

Algorithms for connected p-centdian problem on block graphs 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Combinatorial Optimization Springer Journals

# Algorithms for connected p-centdian problem on block graphs

, Volume 36 (1) – Jul 13, 2016
12 pages

/lp/springer_journal/algorithms-for-connected-p-centdian-problem-on-block-graphs-4i642vf78N
Publisher
Springer Journals
Subject
Mathematics; Combinatorics; Convex and Discrete Geometry; Mathematical Modeling and Industrial Mathematics; Theory of Computation; Optimization; Operations Research/Decision Theory
ISSN
1382-6905
eISSN
1573-2886
D.O.I.
10.1007/s10878-016-0058-0
Publisher site
See Article on Publisher Site

### Abstract

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

Journal of Combinatorial OptimizationSpringer Journals

Published: Jul 13, 2016

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