A Unified View to Greedy Geometric Routing Algorithms in Ad Hoc Networks

Abstract

The main aim of this paper is to give a unified view to greedy geometric routing algorithms in ad hoc networks. For this, we firstly present a general form of greedy routing algorithm using a class of objective functions which are invariant under congruent transformations of a point set. We show that some known greedy routing algorithms such as Greedy Routing, Compass Routing, and Midpoint Routing can be regarded as special cases of the generalized greedy routing algorithm. In addition, inspired by the unified view of greedy routing, we propose three new greedy routing algorithms. We then derive a sufficient condition for our generalized greedy routing algorithm to guarantee packet delivery on every Delaunay graph. This condition makes it easier to check whether a given routing algorithm guarantees packet delivery, and the class of objective functions with this condition is closed under convex combination. We show that Greedy Routing, Midpoint Routing, and the three new greedy routing algorithms proposed in this paper satisfy the sufficient condition, i.e., they guarantee packet delivery on Delaunay graphs, and then compare the merits and demerits of these methods.