The 2-radius and 2-radiian problems on trees

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(n log n)-time algorithm for the 2-radiian problem on trees, where n is the number of vertices in the given tree.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Hung-Lung Wang, Kun-Mao Chao
• Keywords: 2-radius Problem, Facility Location Problems, Non-empty Subsets, TCS 2008, Theoretical Computer Science