Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
A linear-time algorithm for solving the center problem on weighted cactus graphs
Information Processing Letters
The Centdian subtree on tree networks
Discrete Applied Mathematics
Minimizing the sum of the k largest functions in linear time
Information Processing Letters
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Locating facilities on a network to minimize their average service radius
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Efficient algorithms for the weighted 2-center problem in a cactus graph
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Partitioning the nodes of a graph to minimize the sum of subgraph radii
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Hi-index | 5.23 |
In this paper, we consider two facility location problems on tree networks. One is the 2-radius problem, whose goal is to partition the vertex set of the given network into two non-empty subsets such that the sum of the radii of these two induced subgraphs is minimum. The other is the 2-radiian problem, whose goal is to partition the network into two non-empty subsets such that the sum of the centdian values of these two induced subgraphs is minimum. We propose an O(n)-time algorithm for the 2-radius problem on trees and an O(nlogn)-time algorithm for the 2-radiian problem on trees, where n is the number of vertices in the given tree.