A new memoryless online routing algorithm for Delaunay triangulations

Abstract

We consider 1-local online routing on a special class of geometric graphs called Delaunay triangulations (DTs). A geometric graph G = (V, E) of a point set consists of a set of points in the plane and edges between them, where each edge weighs as the Euclidean distance between it’s end-points. DTs are one of the useful classes of these graphs because of some good properties which can help during the navigation process, therefore over the years DTs have been widely proposed as network topologies for several times.In this paper, we present a new memoryless online routing (MOR) algorithm for DTs which is simple, elegant, and easy to implement, while having an acceptable performance.The set of MOR algorithms are suitable for cases where we want to find a path using only local information, our proposed algorithm is memoryless or 1-local, in k-local routing, we find a path between a source vertex s to a destination vertex t while our knowledge at each step is limited to the locations of s and t, the location of current vertex and it’s k-neighborhood vertices.We also evaluate and compare the perforamnce of our prpopsed algorithm with existing MOR algorithms. Our experimental results implied that our proposed algorithm has an acceptable performance in both Euclidean and link metrics and it outperforms all of the existing MOR algorithms in Euclidean metric, and some of them in the link metric as well. Finally, we pose two open problems to solve in the future.