Derandomized graph products

Noga Alon, Uriel Feige, Avi Wigderson, David Zuckerman
1995 Computational Complexity  
Berman and Schnitger [10] gave a randomized reduction from approximating within constant factors arbitrarily close to 1 to approximating clique within a factor of n (for some ). This reduction was further studied by Blum [11], who gave it the name randomized graph products. We show that this reduction can be made deterministic (derandomized), using random walks on expander graphs [1]. The main technical contribution of this paper is in lower bounding the probability that all steps of a random
more » ... lk stay within a specified set of vertices of a graph. (Previous work was mainly concerned with upper bounding this probability.) This lower bound extends also to the case that different sets of vertices are specified for different time steps of the walk.
doi:10.1007/bf01277956 fatcat:xjuibrzzv5eznh5braolfndyki