Face Routing on a Non-Planar Graph: Theory and Applications to Networks

Abstract

In geographic routing protocols, face forwarding is often used in helping a packet escape from the stuck state. To guarantee packet delivery, face forwarding usually routes a packet in a planar subgraph of the network, which might disable many edges in the network and, in turn, worsen the routing performance and reduce the link failure tolerance. In this paper, we aim to improve the connectivity of the graphs on which face forwarding can guarantee packet delivery. We present a sufficient condition for the packet delivery guarantee of GFG face forwarding, augment the graph used in face forwarding with selected disabled edges in the network, and propose a geographic routing protocol, termed GFG-NP, in which a packet escapes from the stuck state by performing GFG face forwarding on the augmented graph that might be non-planar. We show, using theoretical analysis, that GFG-NP guarantees packet delivery when performed on the augmented graphs of the partial Delaunay triangulation (PDT) and the CLDP-stable graph constructed by the cross-link detection protocol (CLDP), termed PDT- and CLDP-augmented graphs, respectively. In addition, simulations on network simulator NS-2 show that GFG-NP with face forwarding performed on PDT- and CLDP-augmented graphs outperforms GFG with face forwarding performed on PDT and the CLDP-stable graph, respectively, in terms of load balance, path length, routing latency, and packet delivery rate.