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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© 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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