The complexity and approximability of minimum contamination problems

Abstract

In this article, we investigate the complexity and approximability of the Minimum Contamination Problems, which are derived from epidemic spreading areas and have been extensively studied recently. We show that both the Minimum Average Contamination Problem and the Minimum Worst Contamination Problem are NP-hard problems even on restrict cases. For any ε > 0, we give (1 + ε, O(1+ε/ε log n))-bicriteria approximation algorithm for the Minimum Average Contamination Problem. Moreover, we show that the Minimum Average Contamination Problem is NP-hard to be approximated within 5/3 - ε and the Minimum Worst Contamination Problem is NP-hard to be approximated within 2 - ε, for any ε > 0, giving the first hardness results of approximation of constant ratios to the problems. © 2011 Springer-Verlag.