Archaeology of random recursive dags and Cooper-Frieze random networks

TL;DR

This paper demonstrates that in large random networks, such as recursive dags and Cooper-Frieze graphs, it is possible to efficiently identify the root vertex with high confidence, regardless of network size.

Contribution

The paper introduces methods to construct size-independent confidence sets for the root in various large random network models.

Findings

Root can be identified with high probability in recursive dags.

Confidence sets are independent of network size.

Applicable to multiple random network models.

Abstract

We study the problem of finding the root vertex in large growing networks. We prove that it is possible to construct confidence sets of size independent of the number of vertices in the network that contain the root vertex with high probability in various models of random networks. The models include uniform random recursive dags and uniform Cooper-Frieze random graphs.