Open Access
February 2017 Looking for vertex number one
Alan Frieze, Wesley Pegden
Ann. Appl. Probab. 27(1): 582-630 (February 2017). DOI: 10.1214/16-AAP1212

Abstract

Given an instance of the preferential attachment graph Gn=([n],En), 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 algorithm which runs in time O(log4n), 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(log4n). We give an algorithm to find vertex 1, which w.h.p. runs in time O(ωlogn) and which is local in the strongest sense of operating only on neighborhoods of single vertices. Here ω=ω(n) is any function that goes to infinity with n.

Citation

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Alan Frieze. Wesley Pegden. "Looking for vertex number one." Ann. Appl. Probab. 27 (1) 582 - 630, February 2017. https://doi.org/10.1214/16-AAP1212

Information

Received: 1 August 2014; Revised: 1 January 2016; Published: February 2017
First available in Project Euclid: 6 March 2017

zbMATH: 1381.60027
MathSciNet: MR3619796
Digital Object Identifier: 10.1214/16-AAP1212

Subjects:
Primary: 60C05

Keywords: local search , preferential attachment graph , Random walk

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.27 • No. 1 • February 2017
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