The Optimal Placement Pattern for Confident Information Coverage in Wireless Sensor Networks

Abstract

Finding the optimal placement pattern to provide complete area coverage is of great theoretical and practical significance. Most of the current studies on placement problem are based on the simplest disk coverage model. In this paper, we study the optimal placement pattern based on the <i>confident information coverage</i> (CIC or <inline-formula><tex-math notation="LaTeX">$\Phi$</tex-math></inline-formula> -coverage) model <xref ref-type="bibr" rid="ref1">[1]</xref> , which is much more complicated than the disk coverage model. Based on the reconstruction theory, the CIC model takes into consideration of not only the collaboration of sensors for information processing but also the spatial correlation of physical phenomena. We first analyze <inline-formula><tex-math notation="LaTeX">$\Phi$</tex-math> </inline-formula> -coverage of one sensor and two sensors, and then <inline-formula><tex-math notation="LaTeX">$\Phi$</tex-math></inline-formula> -coverage of <inline-formula> <tex-math notation="LaTeX">$n$</tex-math></inline-formula> sensors for <inline-formula><tex-math notation="LaTeX">$n \ge 3$</tex-math> </inline-formula> , where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> sensors are deployed at <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> vertices of a regular <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -sided polygon. We prove that the regular triangular lattice is the optimal placement pattern among all the placement patterns consisting of regular polygons. We also extend our analysis to acute cyclic polygons, and prove that the regular triangular lattice is still the optimal placement pattern among all the placement patterns consisting of acute cyclic polygons.