Abstract
The problem of efficiently monitoring the network flow is regarded as the one to find out the minimum weighted weak vertex cover set for a given graph G=(V,E) with weight function w. In this paper, we show that a weak vertex cover set approximating a minimum one within \(2-\frac{2}{\nu(G)}\) can be efficiently found in undirected graphs, and improve the previous work of approximation ratio within ln d + 1, where d is the maximum degree of the vertex in graph G.
This work is supported by a grant from the Ministry of Science and Technology (grant no. 2001CCA03000), National Natural Science Fund (grant no. 60273045) and Shanghai Science and Technology Development Fund (grant no. 03JC14014)
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Zhang, Y., Zhu, H. (2004). An Approximation Algorithm for Weighted Weak Vertex Cover Problem in Undirected Graphs. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_17
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DOI: https://doi.org/10.1007/978-3-540-27798-9_17
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