ABSTRACT
This chapter investigates a fundamental characteristic of a mobile ad hoc network (MANET): the maximum necessary number of hops needed to deliver a packet from a source to a destination. In this chapter, without loss of generality, we assume that the area is a circle with a radius of r , r > 1, and the transmission range of each mobile station is 1. We prove that the maximum necessary number of hops needed to deliver a packet from a source to a destination is 4π√
3 )2 − 1 = 4πr 2√
3 + O(r ) ≈ 7.255r 2 + O(r ). We show that
this result is very close to optimum with only a difference of O(r ).
