Forest Covers and Bounded Forest Covers

Abstract

We study approximation algorithms for the forest cover and bounded forest cover problems. A probabilistic $2+ε$ approximation algorithm for the forest cover problem is given using the method of dual fitting. A deterministic algorithm with a 2-approximation ratio that rounds the optimal solution to a linear program is given next. The 2-approximation for the forest cover is then used to give a 6-approximation for the bounded forest cover problem. The use of the probabilistic method to develop the $2+ε$ approximation algorithm may be of independent interest.

Figures (2)

• Figure 1: Steps to find a forest cover $F$ in $G^*$
• Figure 2: The sub-graphs of $M_{r}^h$ in the sub-component $S_{r}^h$.

Theorems & Definitions (28)

• theorem 1
• proof
• lemma 1
• proof
• lemma 2
• proof
• lemma 3
• proof
• theorem 2
• theorem 3