Abstract
We consider the distributed construction of a minimum weight 2-edge-connected spanning subgraph (2-ECSS) of a given weighted or unweighted graph. A 2-ECSS of a graph is a subgraph that, for each pair of vertices, contains at least two edge-disjoint paths connecting these vertices. The problem of finding a minimum weight 2-ECSS is NP-hard and a natural extension of the distributed MST construction problem, one of the most fundamental problems in the area of distributed computation. We present a distributed \( \frac{3}{2} \)-approximation algorithm for the unweighted 2-ECSS construction problem that requires O( n ) communication rounds and O( m ) messages. Moreover, we present a distributed 3 -approximation algorithm for the weighted 2-ECSS construction problem that requires O( n logn ) communication rounds and O( n log2 n + m ) messages.
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References
Khuller, S., Vishkin, U.: Biconnectivity approximations and graph carvings. J. ACM 41(2), 214–235 (1994)
Jothi, R., Raghavachari, B., Varadarajan, S.: A 5/4-approximation algorithm for minimum 2-edge-connectivity. In: SODA 2003: Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA, Society for Industrial and Applied Mathematics, pp. 725–734 (2003)
Khuller, S., Thurimella, R.: Approximation algorithms for graph augmentation. J. Algorithms 14(2), 214–225 (1993)
Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst. 5(1), 66–77 (1983)
Awerbuch, B.: Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems. In: STOC 1987: Proceedings of the nineteenth annual ACM conference on Theory of computing, pp. 230–240. ACM Press, New York (1987)
Elkin, M.: A faster distributed protocol for constructing a minimum spanning tree. In: SODA 2004: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 359–368 (2004)
Fernandes, C.G.: A better approximation ratio for the minimum k-edge-connected spanning subgraph problem. In: SODA 1997: Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics, pp. 629–638 (1997)
Peleg, D.: Distributed Computing, A Locality-Sensitive Approach. Siam, Philadelphia (2000)
Humblet, P.A.: A distributed algorithm for minimum weight directed spanning trees. IEEE Trans. Comm. 31(6), 756–762 (1983)
Gabow, H., Galil, Z., Spencer, T., Tarjan, R.E.: Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica 6(2), 109–122 (1986)
Pritchard, D.: Robust network computation. Master’s thesis, Massachusetts Institute of Technology (August 2005)
Thurimella, R.: Sub-linear distributed algorithms for sparse certificates and biconnected components (extended abstract). In: PODC 1995: Symposium on Principles of Distributed Computing, pp. 28–37 (1995)
Korman, A.: Labeling schemes for vertex connectivity. In: Arge, L., Gachin, C., Jurdzinshi, T., Taoledci, A. (eds.) ICALP 2007. LNCS, vol. 4596, Springer, Heidelberg (2007)
Gavoille, C.: A survey on interval routing. Theor. Comput. Sci. 245(2), 217–253 (2000)
Bellman, R.: On a routing problem. Quart. Appl. Math. 16, 87–90 (1958)
Alstrup, S., Gavoille, C., Kaplan, H., Rauhe, T.: Nearest common ancestors: a survey and a new distributed algorithm. In: SPAA 2002: Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures, pp. 258–264. ACM Press, New York (2002)
Peleg, D., Rubinovich, V.: A near-tight lower bound on the time complexity of distributed minimum-weight spanning tree construction. SIAM Journal on Computing 30(5), 1427–1442 (2000)
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Krumke, S.O., Merz, P., Nonner, T., Rupp, K. (2007). Distributed Approximation Algorithms for Finding 2-Edge-Connected Subgraphs. In: Tovar, E., Tsigas, P., Fouchal, H. (eds) Principles of Distributed Systems. OPODIS 2007. Lecture Notes in Computer Science, vol 4878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77096-1_12
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DOI: https://doi.org/10.1007/978-3-540-77096-1_12
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