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 Saarbrücken 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.

Abstract—In this paper, we present an implementation of the FairPlay framework for secure two-party function computation on Android smartphones, which we call MobileFairPlay. Mobile-FairPlay allows high-level programming of several secure two-party protocols, including protocols for the Millionaire problem, set intersection, computation of Jaccard similarity coefficient, etc. All these functions are useful in the context of mobile social networks and opportunistic networks, where parties are often requested to exchange sensitive information (list of contacts, interest profiles, etc.) to optimize network operation. To demonstrate the feasibility of MobileFairPlay, we present an application to privacy-preserving interest-casting in opportunistic networks, implementing a recently proposed protocol. We tested running times of the implemented protocol on several Android phones, obtaining very reasonable (up to 5sec) running times. These results clearly promote MobileFairPlay as a feasible security framework for mobile environments. I.