On the Complexity of Finding an Unknown Cut Via Vertex Queries

  • Peyman Afshani
  • Ehsan Chiniforooshan
  • Reza Dorrigiv
  • Arash Farzan
  • Mehdi Mirzazadeh
  • Narges Simjour
  • Hamid Zarrabi-Zadeh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4598)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Peyman Afshani
    • 1
  • Ehsan Chiniforooshan
    • 1
  • Reza Dorrigiv
    • 1
  • Arash Farzan
    • 1
  • Mehdi Mirzazadeh
    • 1
  • Narges Simjour
    • 1
  • Hamid Zarrabi-Zadeh
    • 1
  1. 1.School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1Canada

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