Abstract
Finding a minimum size 2-vertex connected spanning subgraph of a k-vertex connected graph G = (V,E) with n vertices and m edges is known to be NP-hard and APX-hard, as well as approximable in O(n 2 m) time within a factor of 4/3. Interestingly, the problem remains NP-hard even if a Hamiltonian path of G is given as part of the input. For this input-enriched version of the problem, we provide in this paper a linear time and space algorithm which approximates the optimal solution by a factor of no more than min \({\{\frac{5}{4},\frac{2k-1}{2(k-1)}\}}\).
This work has been partially supported by the Research Project GRID.IT, funded by the Italian Ministry of Education, University and Research.
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Bilò, D., Proietti, G. (2005). A \(\frac{5}{4}\)-Approximation Algorithm for Biconnecting a Graph with a Given Hamiltonian Path. In: Persiano, G., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2004. Lecture Notes in Computer Science, vol 3351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31833-0_16
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DOI: https://doi.org/10.1007/978-3-540-31833-0_16
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