Abstract
In this paper we prove, that the minimum cut algorithm presented previously by the author (Brinkmeier 07), requires only linear time with high probability, if the input graph if chosen randomly from the graphs with constant expected degree. In fact a more general lower bound for the probability of a low runtime depending on several parameters is given.
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Bauer, S.: RNA Sekundärstrukturvorhersage. Studienarbeit, TU Ilmenau (April 2004)
Brinkmeier, M.: A simple and fast min-cut algorithm. Theory of Computing Systems 41, 369–380 (2007)
Chekuri, C., Goldberg, A.V., Karger, D.R., Levine, M.S., Stein, C.: Experimental study of minimum cut algorithms. In: Symposium on Discrete Algorithms, pp. 324–333 (1997)
Ford, L.R., Fulkerson, D.R.: Maximal flow through a network. Can. J. Math. 8, 399–404 (1956)
Gabow, H.N.: A matroid approach to finding edge connectivity and packing arborescences. J. Comput. Syst. Sci. 50(2), 259–273 (1995)
Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum flow problem. J. Assoc. Comput. Mach. 35, 921–940 (1988)
Gomory, R.E., Hu, T.C.: Multi-terminal network flows. J. SIAM 9, 551–570 (1961)
Karger, D.R.: Minimum cuts in near-linear time. In: STOC, pp. 56–63 (1996)
Karger, D.R.: Minimum cuts in near-linear time. CoRR, cs.DS/9812007 (1998)
Karger, D.R., Stein, C.: A new approach to the minimum cut problem. J. ACM 43(4), 601–640 (1996)
Matula, D.W.: A linear time 2+epsilon approximation algorithm for edge connectivity. In: SODA, pp. 500–504 (1993)
Nagamochi, H., Ishii, Ibaraki, T.: A simple proof of a minimum cut algorithm and its applications. TIEICE: IEICE Transactions on Communications/Electronics/Information and Systems (1999)
Nagamochi, H., Ibaraki, T.: Computing edge-connectivity in multigraphs and capacitated graphs. SIAM J. Disc. Math. 5(1), 54–66 (1992)
Nagamochi, H., Ibaraki, T.: A linear-time algorithm for finding a sparse k-connected spanning subgraph of a k-connected graph. Algorithmica 7(5&6), 583–596 (1992)
Nagamochi, H., Ibaraki, T.: Graph connectivity and its augmentation: applications of MA orderings. Discrete Applied Mathematics 123(1-3), 447–472 (2002)
Nagamochi, H., Nishimura, K., Ibaraki, T.: Computing all small cuts in undirected networks. In: Du, D.-Z., Zhang, X.-S. (eds.) ISAAC 1994. LNCS, vol. 834, pp. 190–198. Springer, Heidelberg (1994)
Nagamochi, H., Ono, T., Ibaraki, T.: Implementing an efficient minimum capacity cut algorithm. Math. Program. 67, 325–341 (1994)
Padberg, M., Rinaldi, G.: An efficient algorithm for the minimum capacity cut problem. Math. Program. 47, 19–36 (1990)
Stoer, M., Wagner, F.: A simple min-cut algorithm. Journal of the ACM 44(4), 585–591 (1997)
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Brinkmeier, M. (2009). Minimum Cuts of Simple Graphs in Almost Always Linear Time. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_20
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DOI: https://doi.org/10.1007/978-3-642-00202-1_20
Publisher Name: Springer, Berlin, Heidelberg
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