In this paper we provide improved approximation algorithms for the MinMax Tree Cover and Bounded Tree Cover problems. Given a graph G = (V , E) with weights w : In the Min-Max k-tree Cover problem we are given graph G and a positive integer k and the goal is to find a tree cover with k trees, such that the weight of the largest tree in the cover is minimized. We present a 3-approximation algorithm for this improving the two different approximation algorithms presented in Lett. 38:169-173, 2010). In the Bounded Tree Cover problem we are given graph G and a bound λ and the goal is to find a tree cover with minimum number of trees such that each tree has weight at most λ. We present a 2.5-approximation algorithm for this, improving the 3-approximation bound in Arkin et al. (J. Algorithms 59:1-18, 2006).
For min-max tree cover with k trees, Khani and Salavatipour REF later improved the approximation guarantee to a factor of three.
Improved Approximation Algorithms for the Min-max Tree Cover and Bounded Tree Cover Problems
Algorithmica
Algorithmica
Mathematics Computer Science