In this paper we provide improved approximation algorithms for the Min-Max Tree Cover and Bounded Tree Cover problems. Given a graph G = (V,E) with weights w : E → ℕ+, a set T1,T2,...,T k of subtrees of G is called a tree cover of G if V = U i=1k V(Ti). 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 [1,5] with ratio 4. The problem is known to have an APX-hardness lower bound of 3/2 [12]. 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 [1]. © 2011 Springer-Verlag.
CITATION STYLE
Khani, M. R., & Salavatipour, M. R. (2011). Improved approximation algorithms for the min-max tree cover and bounded tree cover problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6845 LNCS, pp. 302–314). https://doi.org/10.1007/978-3-642-22935-0_26
Mendeley helps you to discover research relevant for your work.