Maximum interference of random sensors on a line

Authors:
Evangelos Kranakis;Danny Krizanc;Lata Narayanan;Ladislav Stacho
Affiliations:
School of Computer Science, Carleton University, Ottawa, ON, Canada;Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT;Department of Computer Science and Software Engineering, Concordia University, Montreal, QC, Canada;Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada
Venue:
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Year:
2010

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Abstract

Consider n sensors whose positions are represented by n uniform, independent and identically distributed random variables assuming values in the open unit interval (0,1). A natural way to guarantee connectivity in the resulting sensor network is to assign to each sensor as range the maximum of the two possible distances to its two neighbors. The interference at a given sensor is defined as the number of sensors that have this sensor within their range. In this paper we prove that the expected maximum interference is Ω(ln ln n), and that for any ε0, it is O((ln n)1/2+ε).