Abstract
We investigate the problem of finding an unknown cut through querying vertices of a graph G. Our complexity measure is the number of submitted queries. To avoid some worst cases, we make a few assumptions which allow us to obtain an algorithm with the worst case query complexity of \(O(k)+2k\log{n\over k}\) in which k is the number of vertices adjacent to cut-edges. We also provide a matching lowerbound and then prove if G is a tree our algorithm can asymptotically achieve the information theoretic lowerbound on the query complexity. Finally, we show it is possible to remove our extra assumptions but achieve an approximate solution.
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Blum, A., Chawla, S.: Learning from labeled and unlabeled data using graph mincuts. In: Proceedings of the Eighteenth International Conference on Machine Learning, pp. 19–26. Morgan Kaufmann Publishers, San Francisco (2001)
Blum, A., Lafferty, J., Rwebangira, M.R., Reddy, R.: Semi-supervised learning using randomized mincuts. In: Proceedings of the twenty-first international conference on Machine learning, p. 13. ACM Press, New York (2004)
Joachims, T.: Transductive learning via spectral graph partitioning. In: Twentieth International Conference on Machine Learning (2003)
Joachims, T.: Transductive learning via spectral graph partitioning. In: Proceedings of the International Conference on Machine Learning, pp. 290–297 (2003)
Kamvar, S., Klein, D., Manning, C.: Spectral learning. In: International Joint Conference On Artificial Intelligence (2003)
Kleinberg, J.: Detecting a network failure. In: Proceedings of the Forty-First Annual Symposium on Foundations of Computer Science, p. 231. IEEE Computer Society Press, Los Alamitos (2000)
Mitchell, T.: Machine Learning. McGraw-Hill, New York (1997)
Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: Analysis and an algorithm. Advances in Neural Information Processing Systems (2001)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)
Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised learning using Gaussian fields and harmonic functions. In: Proceedings of the Twentieth International Conference on Machine Learning, pp. 912–919 (2003)
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© 2007 Springer-Verlag Berlin Heidelberg
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Afshani, P. et al. (2007). On the Complexity of Finding an Unknown Cut Via Vertex Queries. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_45
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DOI: https://doi.org/10.1007/978-3-540-73545-8_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73544-1
Online ISBN: 978-3-540-73545-8
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