A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Approximating the tree and tour covers of a graph
Information Processing Letters
A 2-approximation algorithm for the minimum weight edge dominating set problem
Discrete Applied Mathematics
On approximability of the independent/connected edge dominating set problems
Information Processing Letters
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs
SIAM Journal on Computing
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The tree cover (TC) problem is to compute a minimum weight connected edge set, given a connected and edge-weighted graph G, such that its vertex set forms a vertex cover for G. Unlike related problems of vertex cover or edge dominating set, weighted TC is not yet known to be approximable in polynomial time as well as the unweighted version is. Moreover, the best approximation algorithm known so far for weighted TC is far from practical in its efficiency. In this paper we consider a restricted version of weighted TC, as a first step towards better approximation of general TC, where only two edge weights differing by at least a factor of 2 are available. It will be shown that a factor 2 approximation can be attained efficiently (in the complexity of max flow) in this case by a primal-dual method. Even under the limited weights as such, the primal-dual arguments used will be seen to be quite involved, having a nontrivial style of dual assignments as an essential part, unlike the case of uniform weights.