Approximating the longest path length of a stochastic DAG by a normal distribution in linear time

Authors:
Ei Ando;Toshio Nakata;Masafumi Yamashita
Affiliations:
Dept. Computer Sci. and Communication Eng., Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan;Dept. of Mathematics, Fukuoka University of Education, Akama-Bunkyomachi, Munakata, Fukuoka, 811-4192, Japan;Dept. Computer Sci. and Communication Eng., Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan and Institute of Systems, Information Technologies and Nanotechnologies, Fukuoka SRP ...
Venue:
Journal of Discrete Algorithms
Year:
2009

Citing 1
Cited 2

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SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications

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Abstract

This paper presents a linear time algorithm for approximating, in the sense below, the longest path length of a given directed acyclic graph (DAG), where each edge length is given as a normally distributed random variable. Let F(x) be the distribution function of the longest path length of the DAG. Our algorithm computes the mean and the variance of a normal distribution whose distribution function F@?(x) satisfies F@?(x)==a, given a constant a (1/2==F^-^1(a). To evaluate the accuracy of the approximation of F(x) by F@?(x), we first conduct two experiments using a standard benchmark set ITC'99 of logical circuits, since a typical application of the algorithm is the delay analysis of logical circuits. We also perform a worst case analysis to derive an upper bound on the difference F@?^-^1(a)-F^-^1(a).