An Alternative Approach to Find the Fermat Point of a Polygonal Geographic Region for Energy Efficient Geocast Routing Protocols: Global Minima Scheme

Geocasting is a special variant of multicasting, where a data packet is destined for a particular geographic region. For many applications in wireless ad hoc and sensor networks, geocasting is an important and widely used communication service. Many geocast routing protocols with different approachability have been developed. Amongst them the geometry driven approach addresses the usage of an optimum path through the Fermat point of a triangle for packet forwarding. However, the geometry driven scheme faces some practical problems while determining the Fermat point for a polygonal region. Moreover, the method proposed can not be generalized for triangles with an angle more than 120¿. In this paper we discuss a global minima based scheme for finding the Fermat point of a n sided polygonal geographic region, which is more general in its approach and is free from some of the constraints present in the geometry based scheme for finding the Fermat point. Along with that, the present scheme outplays the geometry driven scheme when it comes to the distance traveled by a packet and the energy consumed therefore.