The statistical longest path problem and its application to delay analysis of logical circuits

Abstract

This paper presents an algorithm for estimating, in the sense below, the length of a longest path of a given directed acyclic graph (DAG) whose edge lengths are given as random variables with normal distributions. Let F(x) be the distribution function of the length of a longest path of a given DAG. The algorithm computes a normal distribution function &Ftilde;(x) such that ˜F(x) 〈 F(x) if F(x) 〉 a, given a constant a (0.5 〈 a 〈 1.0). We conduct two experiments to demonstrate the accuracy of &Ftilde;(x).