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arXiv · 1408.6821

Looking for vertex number one

Alan Frieze·Wesley Pegden
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Abstract

Given an instance of the preferential attachment graph $G_n=([n],E_n)$, we would like to find vertex 1, using only 'local' information about the graph; that is, by exploring the neighborhoods of small sets of vertices. Borgs et. al gave an an algorithm which runs in time $O(\log^4 n)$, which is local in the sense that at each step, it needs only to search the neighborhood of a set of vertices of size $O(\log^4 n)$. We give an algorithm to find vertex 1, which w.h.p. runs in time $O(\omega\log n)$ and which is local in the strongest sense of operating only on neighborhoods of single vertices. Here $\omega=\omega(n)$ is any function that goes to infinity with $n$.

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Alan Frieze, Wesley Pegden. 2014-08-28. Looking for vertex number one. https://arxiv.org/abs/1408.6821

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