Approximation hardness of min-max tree covers

Authors:
Zhou Xu;Qi Wen
Affiliations:
Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hong Kong;Department of Management Sciences, The City University of Hong Kong, Hong Kong
Venue:
Operations Research Letters
Year:
2010

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Abstract

We prove the first inapproximability bounds to study approximation hardness for a min-max k-tree cover problem and its variants. The problem is to find a set of k trees to cover vertices of a given graph with metric edge weights, so as to minimize the maximum total edge weight of any of the k trees. Our technique can also be applied to improve inapproximability bounds for min-max problems that use other covering objectives, such as stars, paths, and tours.