Abstract
We study the minimum cut problem in the presence of uncertainty and show how to apply a novel robust optimization approach, which aims to exploit the similarity in subsequent graph measurements or similar graph instances, without posing any assumptions on the way they have been obtained. With experiments we show that the approach works well when compared to other approaches that are also oblivious towards the relationship between the input datasets.
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Buhmann, J.M., Mihalák, M., Šrámek, R., Widmayer, P.: Robust optimization in the presence of uncertainty. In: Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, ITCS 2013, pp. 505–514. ACM, New York (2013)
Botafogo, R.A.: Cluster Analysis for Hypertext Systems. In: Proceedings of the 16th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 116–125. ACM (1993)
Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(9), 1124–1137 (2004)
Ramanathan, A., Colbourn, C.J.: Counting almost minimum cutsets with reliability applications. Mathematical Programming 39(3), 253–261 (1987)
Schneider, J.J., Kirkpatrick, S.: Stochastic Optimization. Springer (2007)
Kall, P., Mayer, J.: Stochastic Linear Programming: Models, Theory, and Computation. Springer (2005)
Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton Series in Applied Mathematics. Princeton University Press (October 2009)
Bilu, Y., Linial, N.: Are stable instances easy? In: Proceedings of the First Symposium on Innovations in Computer Science (ICS), pp. 332–341 (2010)
Bilò, D., Böckenhauer, H.-J., Hromkovič, J., Královič, R., Mömke, T., Widmayer, P., Zych, A.: Reoptimization of steiner trees. In: Gudmundsson, J. (ed.) SWAT 2008. LNCS, vol. 5124, pp. 258–269. Springer, Heidelberg (2008)
Mihalák, M., Schöngens, M., Šrámek, R., Widmayer, P.: On the complexity of the metric TSP under stability considerations. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 382–393. Springer, Heidelberg (2011)
Mihalák, M., Šrámek, R.: Counting approximately-shortest paths in directed acyclic graphs (2013), http://arxiv.org/abs/1304.6707
Dinits, E.A., Karzanov, A.V., Lomonosov, V.: On the Structure of a Family of Minimal Weighted Cuts in a Graph (1976)
Karger, D.R.: Global min-cuts in RNC, and other ramifications of a simple min-out algorithm. In: Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 21–30 (1993)
Scott Provan, J., Ball, M.O.: The complexity of counting cuts and of computing the probability that a graph is connected. SIAM Journal on Computing 12(4), 777–788 (1983)
Nagamochi, H., Nishimura, K., Ibaraki, T.: Computing all small cuts in an undirected network. SIAM Journal on Discrete Mathematics 10(3), 469–481 (1997)
Karger, D.R., Stein, C.: A new approach to the minimum cut problem. Journal of the ACM 43(4), 601–640 (1996)
Geissmann, B.: Approximation set optimization for minimum cut (August 2012), http://www.100acrewood.org/~rasto/publications/ThesisBarbaraGeissmann.pdf
Market rates online (August 2012), http://www.marketratesonline.com
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Geissmann, B., Šrámek, R. (2014). Finding Robust Minimum Cuts. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_12
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DOI: https://doi.org/10.1007/978-3-319-07956-1_12
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