Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Information Processing Letters
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Operations Research Letters
Optimal strategies for the one-round discrete Voronoi game on a line
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Particle swarm optimization with two swarms for the discrete (r|p)-centroid problem
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
A Stackelberg solution for fuzzy random competitive location problems with demand site uncertainty
Intelligent Decision Technologies
Optimal strategies for the one-round discrete Voronoi game on a line
Journal of Combinatorial Optimization
Hi-index | 5.23 |
An instance of the (r,p)-centroid problem is given by an edge and node weighted graph. Two competitors, the leader and the follower, are allowed to place p and r facilities, respectively, into the graph. Users at the nodes connect to the closest facility. A solution of the (r,p)-centroid problem is a leader placement such that the maximum total weight of the users connecting to any follower placement is as small as possible. We show that the absolute (r,p)-centroid problem is NP-hard even on a path which answers a long-standing open question of the complexity of the problem on trees (Hakimi, 1990 [10]). Moreover, we provide polynomial time algorithms for the discrete (r,p)-centroid on paths and the (1,p)-centroid on trees, and complementary hardness results for more complex graph classes.