Local Routing in Convex Subdivisions

In various wireless networking settings, node locations determine a network’s topology, allowing the network to be modelled by a geometric graph drawn in the plane. Without any additional information, local geometric routing algorithms can guarantee delivery to the target node only in restricted classes of geometric graphs, such as triangulations. In order to guarantee delivery on more general classes of geometric graphs (e.g., convex subdivisions or planar subdivisions), previous local geometric routing algorithms required [Formula: see text] state bits to be stored and passed with the message. We present the first local geometric routing algorithm using only one state bit to guarantee delivery on convex subdivisions and, when the algorithm has knowledge of the incoming port (the preceding node on the route), the first stateless local geometric routing algorithm that guarantees delivery on edge-augmented monotone subdivisions (including all convex subdivisions). We also show that [Formula: see text] state bits are necessary in planar subdivisions in which faces may have three or more reflex vertices.

A Modified Kruskal's Algorithm to Improve Genetic Search for Open Vehicle Routing Problem

This article has proposed a modified Kruskal's method to increase the efficiency of a genetic algorithm to determine the path of least distance starting from a central point to solve the open vehicle routing problem. In a vehicle routing problem, vehicles start from a central point and several customers placed in different locations to serve their demands and return to the central point. In the case of the open vehicle routing problem, the vehicles do not go back to the central point after serving the customers. The challenge is to reduce the number of vehicles used and the distance travelled simultaneously. The proposed method applies genetic algorithms to find the set of customers those are covered by a particular vehicle and the authors have applied the proposed modified Kruskal's method for local routing optimization. The results of the new method are analyzed in comparison with some of the evolutionary methods.