On the Complexity of Finding an Unknown Cut Via Vertex Queries

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.

• Type: Conference
• Year: 2007
• Where: COCOON
• Authors: Peyman Afshani, Ehsan Chiniforooshan, Reza Dorrigiv, Arash Farzan, Mehdi Mirzazadeh, Narges Simjour, Hamid Zarrabi-Zadeh
• Keywords: Case Query Complexity, COCOON 2007, Query Complexity, Worst Case