Local Routing in Convex Subdivisions

Low Memory Local Geometric Routing with Guaranteed Delivery in Monotone Subdivisions

“…Consequently, to guarantee delivery on classes of graphs beyond triangulations requires additional information provided, for example, by predecessor-awareness or state bits modified dynamically during routing. Using a single state bit (and without predecessor-awareness), Bose et al [4] presented a deterministic local geometric routing algorithm called OneBit that guarantees delivery on convex subdivisions (assuming general position of vertex coordinates). The key observation is that if we draw a vertical line through the destination, due to the geometry of convex faces, we can route along the boundary of an ever-decreasing closed region that contains the destination.…”

“…Various models represent wireless networks as a graph, representing nodes as points in the plane and direct wireless communication links as edges connecting the corresponding pairs of nodes. The inherent geometry of these graphs enables efficient routing algorithms to be developed (e.g., [2,4,5,6,8,10]) using fewer resources (memory, computational, etc.) than is possible without geometry in general graphs.…”

“…In order to successfully find a path in point-to-point routing, some algorithms store state information at visited nodes to be used and updated if the message ever returns to that node. A memoryless algorithm is one that does not persistently store any state information at visited nodes [4]; once the message leaves the node it is as if the node had never seen the message.…”

“…When there are bits in that extra memory that represent the state of the algorithm, those bits are referred to as state bits. A stateless routing algorithm is one that passes no state bits along in the message header for the purpose of routing [4]. We will only discuss algorithms in which the extra storage bits are either state bits or bits used to represent nodes (e.g., storing the coordinates of the predecessor or origin of the message).…”

“…A local geometric routing algorithm is one that makes forwarding decisions based on knowledge of the position of the node currently handling the message as well as the positions of its direct neighbours, i.e. the neighbours it is directly connected to by a link [4]. Nodes in this model know that the neighbours exist as well as their positions, and the message header contains the coordinates of the destination.…”