Strong connectivity in sensor networks with given number of directional antennae of bounded angle

Authors:
Stefan Dobrev;Evangelos Kranakis;Danny Krizanc;Jaroslav Opatrny;Oscar Morales Ponce;Ladislav Stacho
Affiliations:
Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovak Republic;School of Computer Science, Carleton University, Ottawa, ON, Canada;Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT;Department of Computer Science, Concordia University, Montréal, QC, Canada;School of Computer Science, Carleton University, Ottawa, ON, Canada;Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada
Venue:
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Year:
2010

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Abstract

Given a set S of n sensors in the plane we consider the problem of establishing an ad hoc network from these sensors using directional antennae. We prove that for each given integer 1 ≤ k ≤ 5 there is a strongly connected spanner on the set of points so that each sensor uses at most k such directional antennae whose range differs from the optimal range by a multiplicative factor of at most 2 ċ sin(π/k+1). Moreover, given a minimum spanning tree on the set of points the spanner can be constructed in additional O(n) time. In addition, we prove NP completeness results for k = 2 antennae.