Abstract
The problem of finding a minimum biconnected spanning subgraph of an undirected graph is NP-hard. This paper, improving a chain of work [1, 10, 3, 4], gives the first NC algorithm for approximating a minimum biconnected subgraph with an approximation factor approaching 3/2. This result matches the performance of the currently best sequential approximation algorithm [7].
This research was supported by Hong Kong RGC Grant 338/065/0027.
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References
J. Cheriyan and R. Thurimella, Algorithms for Parallel k-Vertex Connectivity and Sparse Certificates, STOC, 1991, pp. 391–401.
K.W. Chong and T.W. Lam, Finding Connected Components in O(log n loglog n) time on the EREW PRAM, Journal of Algorithms, 1995, pp. 378–402.
K.W. Chong and T.W. Lam, Approximating Biconnectivity in Parallel, SPAA, 1995, pp. 224–233.
K.W. Chong and T.W. Lam, Improving Biconnectivity Approximation via Local Optimization, SODA, 1996, pp. 26–35.
T. Fischer, A.V. Goldberg, D.J. Haglin, and S. Plotkin, Approximating Matchings in Parallel, Information Processing Letter, 46(1993), pp. 115–118.
M.R. Garey and D.B. Johnson, Computers and Intractability: A guide to the theory of NP-completeness, Freeman, San Francisco, 1978.
N. Garg, V.S. Santosh, and A. Singla, Improved Approximation Algorithms for Biconnected Subgraphs via Better Lower Bounding Techniques, SODA, 1993, pp. 103–111.
R.M. Karp and V. Ramachandran, Parallel Algorithms for Shared-Memory Machines, Handbook of Theoretical Computer Science, vol A, J. van Leeuwen Ed., MIT Press, Massachusetts, 1990, pp. 869–941.
V. Vazirani, Parallel graph matching, Synthesis of Parallel Algorithms, J.H. Reif Ed., Morgan Kaufmann, San Mateo, CA, 1991.
P. Kelsen and V. Ramachandran, On Finding Minimal 2-Connected Subgraphs, Journal of Algorithms, 1995, pp. 1–49.
S. Khuller and U. Vishkin, Biconnectivity approximations and graph carvings, Journal of ACM, Vol. 41 No. 2, 1994, pp. 214–235.
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© 1996 Springer-Verlag Berlin Heidelberg
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Chong, K.W., Lam, T.W. (1996). Towards more precise parallel biconnectivity approximation. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009498
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DOI: https://doi.org/10.1007/BFb0009498
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