On the complexity of finding an unknown cut via vertex queries

Authors:
Peyman Afshani;Ehsan Chiniforooshan;Reza Dorrigiv;Arash Farzan;Mehdi Mirzazadeh;Narges Simjour;Hamid Zarrabi-Zadeh
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada
Venue:
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Year:
2007

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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/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.