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arXiv · 1101.5547

Longest path distance in random circuits

Nicolas Broutin·Omar Fawzi
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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 exists 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 (2009+). 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.

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Nicolas Broutin, Omar Fawzi. 2012-05-28. Longest path distance in random circuits. https://doi.org/10.1017/s0963548312000260

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