Multihop Wireless Networks: Opportunistic Routing

2.2 Principles of Local Behavior of GOR

2.2.1 EPA Strictly Increasing Property

Intuitively, increasing the number of forwarding candidates would result in a larger EPA. We present Lemma 2.1 to confirm this intuition.

 

Definition 2.1 Define EM() be the maximum EPA (defined in Equation (2.1)) achieved by selecting r forwarding candidates from .

 

Lemma 2.1 (Strictly increasing property) EM is a strictly increasing function of r.

 

Proof. Assume 1 ≤ m < n ≤ M, and without loss of generality, let be the ordered node set achieving EM with forwarding priority i1 >…> im. We then select a subset with n − m nodes from the remaining node set {im+1, im+2, …, iM}, say . Assume we retain the relay priority of the m nodes in unchanged and give the nodes in lower priorities than those in . Then in , we ...