Vol 1 No 2 (2006)
Articles

Constructing Incremental Sequences in Graphs

Ralf Klasing
LaBRI - Université Bordeaux
Christian Laforest
IBISC, Université d’Evry
Joseph Peters
School of Computing Science, Simon Fraser University
Nicolas Thibault
IBISC, Université d’Evry
Published June 30, 2006
Keywords
  • incremental sequence,
  • graph,
  • approximation algorithms
How to Cite
Klasing, R., Laforest, C., Peters, J., & Thibault, N. (2006). Constructing Incremental Sequences in Graphs. Algorithmic Operations Research, 1(2). Retrieved from https://journals.lib.unb.ca/index.php/AOR/article/view/666

Abstract

Given a weighted graph , we investigate the problem of constructing a sequence of subsets of vertices (called groups) with small diameters, where the diameter of a group is calculated using distances in G. The constraint on these n groups is that they must be incremental: . The cost of a sequence is the maximum ratio between the diameter of each group Mi and the diameter of a group with I vertices and minimum diameter:

.

This quantity captures the impact of the incremental constraint on the diameters of the groups in a sequence. We give general bounds on the value of this ratio and we prove that the problem of constructing an optimal incremental sequence cannot be solved approximately in polynomial time with an approximation ratio less than 2 unless P = NP. Finally, we give a 4-approximation algorithm and we show that the analysis of our algorithm is tight.