Scalable routing easy as PIE: A practical isometric embedding protocol

Abstract

Abstract-We present PIE, a scalable routing scheme that achieves 100% packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual coordinates in a space of concise dimensionality, which enables greedy routing based only on local knowledge. PIE is a general routing scheme, meaning that it works on any graph. We focus however on the Internet, where routing scalability is an urgent concern. We show analytically and by using simulation that the scheme scales extremely well on Internet-like graphs. In addition, its geometric nature allows it to react efficiently to topological changes or failures by finding new paths in the network at no cost, yielding better delivery ratios than standard algorithms. The proposed routing scheme needs an amount of memory polylogarithmic in the size of the network and requires only local communication between the nodes. Although each node constructs its coordinates and routes packets locally, the path stretch remains extremely low, even lower than for centralized or less scalable state-of-the-art algorithms: PIE always finds short paths and often enough finds the shortest paths.

Greedy Zone Routing: Robust and Scalable Routing in Wireless Ad-hoc Networks

“…There are several attempts to overcome this by introducing multiple trees embedded instead of a single spanning tree [15], [5]. This suggests a node to hold multiple coordinates, corresponding to different spanning trees.…”

“…We use the isometric tree embedding scheme proposed in PIE [5] to perform the greedy zone embedding. Compared to the embedding on hyperbolic spaces, coordinate computation in PIE is efficient and can be done in a distributed fashion.…”

“…An important consideration in greedy embedding is to accord the combinatorial properties of a communication graph with the corresponding geometry. In [4], [5], [17], a spanning tree of the network is extracted and the greedy embedding accordingly constructed. Therefore, once the embedding is constructed, changes in the underlying communication graph (hence the spanning tree) can disturb the greedy properties, which is a major drawback in this approach.…”

“…The coordinate assignment of PIE [5] starts by assigning 0 to the root node. Then it recursively assigns the coordinates to the descendants of the tree as follows: the parent node u enumerates its children and produces a binary map b of them.…”

“…Initially, existence of greedy embeddings was shown for special classes of graphs. Subsequently it was shown in [4], [5] for arbitrarily connected graphs. These approaches to greedy embedding extract a spanning tree of the network and assign coordinates such that hop distances on the tree are preserved.…”