Annals of Operations Research

, Volume 110, Issue 1, pp 69–82

A Note on the Robust 1-Center Problem on Trees

  • Rainer E. Burkard
  • Helidon Dollani

DOI: 10.1023/A:1020711416254

Cite this article as:
Burkard, R.E. & Dollani, H. Annals of Operations Research (2002) 110: 69. doi:10.1023/A:1020711416254


We consider the robust 1-center problem on trees with uncertainty in vertex weights and edge lengths. The weights of the vertices and the lengths of the edges can take any value in prespecified intervals with unknown distribution. We show that this problem can be solved in O(n3 log n) time thus improving on Averbakh and Berman's algorithm with time complexity O(n6). For the case when the vertices of the tree have weights equal to 1 we show that the robust 1-center problem can be solved in O(nlog n) time, again improving on Averbakh and Berman's time complexity of O(n2 log n).

location problemsrobust optimizationcenter problem

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Rainer E. Burkard
    • 1
  • Helidon Dollani
    • 1
  1. 1.Institut für Mathematik BTechnische Universität GrazGrazAustria