Geometric Routing Without Geometry

Abstract

In this paper we propose a new routing paradigm, called pseudo-geometric routing. In pseudo-geometric routing, each node u of a network of computing elements is assigned a pseudo coordinate composed of the graph (hop) distances from u to a set of designated nodes (the anchors) in the network. On theses pseudo coordinates we employ greedy geometric routing. Almost as a side effect, pseudo-geometric routing is not restricted to planar unit disk graph networks anymore, but succeeds on general networks.

Routing in Wireless Networks with Position Trees

“…The main result states that the number of beacons needed to get the set fixed is linear on the number of nodes, hence a logical coordinate system must use O(n) such reference points, and consequently must use O(n) space to store the labels. Our result is in line with the bounds given in [19] for nodes in general position. The key difference is that we encode the labels in a different way, using only O(log n) space to represent each label.…”

“…With hop counting, the labels or identifiers obtained are not unique while the routing algorithms rely on the uniqueness of the labels. The authors of [19] studies the number of these reference points needed to avoid duplicate labels. The main result states that the number of beacons needed to get the set fixed is linear on the number of nodes, hence a logical coordinate system must use O(n) such reference points, and consequently must use O(n) space to store the labels.…”

Geometric algorithms for sensor networks

“…To conclude, we remark that a few other protocols, whose ideas are similar to one of these, were not covered in detail here [89,98]. The landmarks in these schemes are mainly used as points of reference, and do not serve the functionalities of gateway nodes (which attract traffic).…”

Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts

“…Some applications do not require the realization of a unit disk graph. For example, georouting can be facilitated by pseudogeometric coordinates (see [23]). An algorithm for pseudogeometric coordinates selects several nodes, a 1 , .…”