Remarks on Category-Based Routing in Social Networks

TL;DR

This paper improves theoretical bounds on category-based routing in social networks, demonstrating how to assign categories to enable efficient greedy message passing based on local information.

Contribution

It significantly refines the upper bounds and establishes new lower bounds for category assignments needed for greedy routing in social network models.

Findings

Improved upper bounds on category assignments for routing

New lower bounds demonstrating limitations of category-based routing

Enhanced understanding of the sociological plausibility of routing models

Abstract

It is well known that individuals can route messages on short paths through social networks, given only simple information about the target and using only local knowledge about the topology. Sociologists conjecture that people find routes greedily by passing the message to an acquaintance that has more in common with the target than themselves, e.g. if a dentist in Saarbr\"ucken wants to send a message to a specific lawyer in Munich, he may forward it to someone who is a lawyer and/or lives in Munich. Modelling this setting, Eppstein et al. introduced the notion of category-based routing. The goal is to assign a set of categories to each node of a graph such that greedy routing is possible. By proving bounds on the number of categories a node has to be in we can argue about the plausibility of the underlying sociological model. In this paper we substantially improve the upper bounds introduced by Eppstein et al. and prove new lower bounds.