Labeling Algorithm and Compact Routing Scheme for a Small World Network Model
Santiago Viertel, Andr\'e Lu\'is Vignatti

TL;DR
This paper introduces a labeling algorithm and a compact routing scheme for a small world network model based on a torus with random edges, enabling efficient routing by identifying the underlying topology.
Contribution
It proposes a linear time labeling algorithm that detects the torus structure in a small world network with random edges, facilitating compact routing schemes.
Findings
Small probability of forbidden cycles allows topology detection.
Breadth-first search effectively finds vertex positions on the torus.
The labeling algorithm enables efficient greedy routing in the network.
Abstract
This paper defines the toroidal small world labeling problem that asks for a labeling of the vertices of a network such that the labels possess information that allows a compact routing scheme in the network. We consider the problem over a small world network model we propose. Both the model and the compact routing scheme have applications in peer-to-peer networks. The proposed model is based on the model of Kleinberg (2000), and generates an undirected two-dimensional torus with one random long-range edge per vertex. These random edges create forbidden cycles that mimic the underlying torus topology, and this behavior confuses attempts for extracting the routing information from the network. We show that such forbidden cycles happen with small probability, allowing us to use a breadth-first search that finds the vertices positions on the torus. The positions are pairs of integer…
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Taxonomy
TopicsPeer-to-Peer Network Technologies · Complex Network Analysis Techniques · Stochastic processes and statistical mechanics
