Abstract
Given a graph G=(V,E) and a tree T=(V,F) with E∩F=∅ such that G + T = (V,F∪E) is 2-edge-connected, we consider the problem of finding a smallest 2-edge-connected spanning subgraph (V,F∪\( E' \)) of G + T containing T. The problem, which is known to be NP-hard, admits a 2-approximation algorithm. However, obtaining a factor better than 2 for this problem has been one of the main open problems in the graph augmentation problem. In this paper, we present an O \( \left( {\sqrt n m} \right) \) time \( \frac{{12}} {7} \)-approximation algorithm for this problem, where \( n = \left| V \right| \) and \( m = \left| {E \cup F} \right| \)
This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan, and the subsidy from the Inamori Foundation.
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Nagamochi, H., Ibaraki, T. (1999). An Approximation for Finding a Smallest 2-Edge-Connected Subgraph Containing a Specified Spanning Tree. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_3
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DOI: https://doi.org/10.1007/3-540-48686-0_3
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