Succinct Greedy Geometric Routing in the Euclidean Plane

TL;DR

This paper presents a new succinct embedding method for 3-connected planar graphs in the Euclidean plane, enabling efficient greedy geometric routing with minimal coordinate size, reducing bandwidth and header overhead.

Contribution

It introduces a succinct coordinate system for greedy routing in planar graphs embedded in R^2, supporting efficient distance comparisons with O(log n) bits per node.

Findings

Existence of greedy routing schemes for 3-connected planar graphs in R^2.

Coordinates can be represented with O(log n) bits, supporting efficient routing.

Significant reduction in bandwidth, space, and header size compared to previous methods.

Abstract

In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. We show that greedy geometric routing schemes exist for the Euclidean metric in R^2, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(log n) bits, where n is the number of vertices in the graph. Moreover, our embedding strategy introduces a coordinate system for R^2 that supports distance comparisons using our succinct coordinates. Thus, our scheme can be used to significantly reduce bandwidth, space, and header size over other recently discovered greedy geometric routing implementations for R^2.