Connectivity of Wireless Sensor Networks with Constant Density

We consider a wireless sensor network in which each sensor is able to transmit within a disk of radius one. We show with elementary techniques that there exists a constant c such that if we throw cN sensors into an n × n square (of area N) independently at random, then with high probability there will be exactly one connected component which reaches all sides of the square. Its expected size is a constant fraction of the total number of sensors, and it covers a constant fraction of the area of the square. Furthermore, the other connected components of sensors and uncovered contiguous portions of the square are each very small (O(log2 n) and O(log N) respectively), so that their relative size grows smaller as N increases. We also discuss some algorithmic implications.

• Type: Conference
• Year: 2004
• Where: ADHOCNOW
• Authors: Sarah Carruthers, Valerie King
• Keywords: ADHOCNOW 2004, Constant Fraction, Sensors, Wireless Networks, Wireless Sensor Network