Showing papers by "Andrei Z. Broder published in 1988"

Bounds on the cover time

Abstract: A particle that moves on a connected unidirected graph G with n vertices is considered. At each step the particle goes from the current vertex to one of its neighbors, chosen uniformly at random. The cover time is the first time when the particle has visited all the vertices in the graph, starting from a given vertex. Upper and lower bounds are presented that relate the expected cover time for a graph to the eigenvalues of the Markov chain that describes the above random walk. An interesting consequence is that regular expander graphs have expected cover time theta (n log n). >

On Generating Solved Instances of Computational Problems

Abstract: We consider the efficient generation of solved instances of computational problems. In particular, we consider invulnerable generators. Let S be a subset of 0,1* and M be a Turing Machine that accepts S; an accepting computation w of M on input x is called a “witness” that x ∈ S. Informally, a program is an α-invulnerable generator if, on input 1n, it produces instance-witness pairs , with |x| = n, according to a distribution under which any polynomial-time adversary who is given x fails to find a witness that x ∈ S, with probability at least α, for infinitely many lengths n.