Acyclic Preference Systems in P2P Networks

TL;DR

This paper investigates acyclic preference systems in P2P networks, showing they can be represented with symmetric matrices and often form small-world graphs, which has implications for network stability and efficiency.

Contribution

It introduces a method to represent and merge acyclic preference systems using symmetric matrices and analyzes their structural properties in P2P networks.

Findings

Acyclic preference systems can be represented with symmetric mark matrices.

Stable configurations often form small-world graphs.

Preferences based on real latency measurements lead to small-world stable configurations.

Abstract

In this work we study preference systems natural for the Peer-to-Peer paradigm. Most of them fall in three categories: global, symmetric and complementary. All these systems share an acyclicity property. As a consequence, they admit a stable (or Pareto efficient) configuration, where no participant can collaborate with better partners than their current ones. We analyze the representation of the such preference systems and show that any acyclic system can be represented with a symmetric mark matrix. This gives a method to merge acyclic preference systems and retain the acyclicity. We also consider such properties of the corresponding collaboration graph, as clustering coefficient and diameter. In particular, studying the example of preferences based on real latency measurements, we observe that its stable configuration is a small-world graph.