Improved approximation algorithms for the min-max tree cover and bounded tree cover problems

Authors:
M. Reza Khani;Mohammad R. Salavatipour
Affiliations:
Dept. of Computing Science, Univ. of Alberta;Toyota Tech. Inst. at Chicago, and Dept. of Computing Science, Univ. of Alberta
Venue:
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Year:
2011

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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 T1, T2,..., Tk of subtrees of G is called a tree cover of G if V = ∪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 APXhardness 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].