Abstract
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 T 1,T 2,…,T k of subtrees of G is called a tree cover of G if \(V=\bigcup_{i=1}^k V(T_i)\). 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 \(\frac{3}{2}\) [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].
The authors were supported by NSERC. Work of the second author was additionally supported by an Alberta Ingenuity New Faculty Award.
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Khani, M.R., Salavatipour, M.R. (2011). Improved Approximation Algorithms for the Min-Max Tree Cover and Bounded Tree Cover Problems. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2011 2011. Lecture Notes in Computer Science, vol 6845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22935-0_26
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DOI: https://doi.org/10.1007/978-3-642-22935-0_26
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