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Longest Path Distance in Random Circuits

Published online by Cambridge University Press:  03 July 2012

NICOLAS BROUTIN  and
OMAR FAWZI
NICOLAS BROUTIN
Affiliation:
INRIA Rocquencourt, 78153 Le Chesnay, France (e-mail: nicolas.broutin@inria.fr)
OMAR FAWZI
Affiliation:
School of Computer Science, McGill University, H3A 2K6, Montreal, Canada (e-mail: ofawzi@cs.mcgill.ca)
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Abstract

We study distance properties of a general class of random directed acyclic graphs (dags). In a dag, many natural notions of distance are possible, for there exist multiple paths between pairs of nodes. The distance of interest for circuits is the maximum length of a path between two nodes. We give laws of large numbers for the typical depth (distance to the root) and the minimum depth in a random dag. This completes the study of natural distances in random dags initiated (in the uniform case) by Devroye and Janson. We also obtain large deviation bounds for the minimum of a branching random walk with constant branching, which can be seen as a simplified version of our main result.

Keywords

Primary 60C0505C0594D99

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 6 , November 2012 , pp. 856 - 881
Copyright
Copyright © Cambridge University Press 2012

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