Morelia Test: Improving the Efficiency of the Gabriel Test and Face Routing in Ad-Hoc Networks

Routing and Traversal via Location Awareness in Ad Hoc Networks

“…We subdivide the area of the circle with diameter AB into four regions X 1 , X 2 , Y 1 and Y 2 (see Figure 6) as determined by an arc of radius R. Figure 7 depicts several scenarios being considered prior to determining whether or not an edge should be deleted. Details of the precise specification of the Morelia test applied to a link AB can be found in Boone et al [3].…”

“…In this section, we describe two procedures for constructing a geometric spanner in a given ad-hoc network: the Gabriel test is due to Bose et al [5] and the Morelia test is due to Boone et al [3].…”

Routing in Wireless Networks with Position Trees

“…Since the path length depends on the planar subgraph extracted, we compared RPT with RNG [31], Gabriel Graph [13], Morelia Graph [4] and the virtual spanner [30,29]. Please note that GFG relies on an external location service like GPS.…”

Energy efficient geographic routing for wireless sensor networks.

“…For a given network topology, several distributed algorithms [17][18][19][20] are available to planarize a network topology. In these algorithms, each node autonomously eliminates its connections (i.e., edges) to its neighbors from the consideration of the routing based on the locations of the neighbors so that the network topology contains no cross edges.…”

“…In the Relative Neighborhood Graph (RNG) [19], a node 11 eliminates a link to a neighbor v if there exists at least one node in the intersection of radio coverages of 11 and v. In the Gabriel Graph (GG) [17], a node 11 eliminates a link to a neighbor v if there exists at least one node in the circle with diameteruv. The Planar Spanner in [18] and the Morelia test in [20] employ more complicated algorithms to compute the planar graph so that a smaller number of edges are deleted from the original topology. Note that, the edge elimination process in graph planarization has two potentially negative impacts to the routing.…”