Smallest number of sensors for k-Covering

Abstract

This paper presents some theoretical results on the smaller number Nk(a, b) of sensors to achieve k coverage for the rectangular area [0, a] × [0, b]. The first properties show the numbers Nk(a, b) are sub-additive and increasing on each variable. Based on these results, some lower and upper bounds for Nk(a, b) are introduced. The main result of the article proves that the minimal density of sensors to achieve k-coverage is λ(k) ≤ k/2 improving a previous result of Ammari and Das [2]. Finally, the numbers N1(a, b) are tabled for some small values of a, b. © 2006-2013 by CCC Publications.