Forest Covers and Bounded Forest Covers

TL;DR

This paper presents new approximation algorithms for forest cover and bounded forest cover problems, including a probabilistic $2+ ext{epsilon}$ and a deterministic 2-approximation, advancing solution quality for these problems.

Contribution

It introduces a probabilistic $2+ ext{epsilon}$ approximation algorithm and a deterministic 2-approximation algorithm for forest cover, and extends the approach to bounded forest cover.

Findings

Probabilistic $2+ ext{epsilon}$ approximation achieved.

Deterministic 2-approximation algorithm developed.

Bounded forest cover approximation improved to 6-approximation.

Abstract

We study approximation algorithms for the forest cover and bounded forest cover problems. A probabilistic $2+\epsilon$ 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 $2+\epsilon$ approximation algorithm may be of independent interest.