Papillon: Greedy Routing in Rings

TL;DR

This paper introduces a new network design for ring-structured nodes that enables greedy routing to operate in logarithmic hops, optimizing routing efficiency in peer-to-peer and social network models.

Contribution

The paper presents the first network over n nodes with greedy routing taking O(log n / log d) hops, achieving asymptotic optimality and improving upon previous O(log^2 n / d) bounds.

Findings

Greedy routing in the constructed network takes O(log n / log d) hops.

The network design is asymptotically optimal for greedy routing.

Previous methods required O(log^2 n / d) hops.

Abstract

We study {\sc greedy} routing over $n$ nodes placed in a ring, with the \emph{distance} between two nodes defined to be the clockwise or the absolute distance between them along the ring. Such graphs arise in the context of modeling social networks and in routing networks for peer-to-peer systems. We construct the first network over $n$ nodes in which {\sc greedy} routing takes $O(\log n / \log d)$ hops in the worst-case, with $d$ out-going links per node. Our result has the first asymptotically optimal greedy routing complexity. Previous constructions required $O(\frac{\log^2 n}{d})$ hops.