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A Generalized Cover Time for Random Walks on Graphs

In: Formal Power Series and Algebraic Combinatorics

Author

Listed:
  • Cyril Banderier

    (INRIA (Rocquencourt), Algorithms Project)

  • Robert P. Dobrow

    (Clarkson University)

Abstract

Given a random walk on a graph, the cover time is the first time (number of steps) that every vertex has been hit (covered) by the walk. Define the marking time for the walk as follows. When the walk reaches vertex vi, a coin is flipped and with probability pi the vertex is marked (or colored). We study the time that every vertex is marked. (When all the pi’s are equal to 1, this gives the usual cover time problem.) General formulas are given for the marking time of a graph. Connections are made with the generalized coupon collector’s problem. Asymptotics for small p i ’s are given. Techniques used include combinatorics of random walks, theory of determinants, analysis and probabilistic considerations.

Suggested Citation

  • Cyril Banderier & Robert P. Dobrow, 2000. "A Generalized Cover Time for Random Walks on Graphs," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 113-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_10
    DOI: 10.1007/978-3-662-04166-6_10
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