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Reliable broadcast is a communication primitive guaranteeing, intuitively, that all processes in a distributed system deliver the same set of messages. The reason why this primitive is appealing is twofold: (i) we can implement it deterministically in a completely asynchronous environment, unlike stronger primitives like consensus and total-order broadcast, and yet (ii) reliable broadcast is powerful enough to implement important applications like payment systems. The problem we tackle in this paper is that of dynamic reliable broadcast, i.e., enabling processes to join or leave the system. This property is desirable for long-lived applications (aiming to be highly available), yet has been precluded in previous asynchronous reliable broadcast protocols. We study this property in a general adversarial (i.e., Byzantine) environment. We introduce the first specification of a dynamic Byzantine reliable broadcast (DBRB) primitive that is amenable to an asynchronous implementation. We then present an algorithm implementing this specification in an asynchronous network. Our DBRB algorithm ensures that if any correct process in the system broadcasts a message, then every correct process delivers that message unless it leaves the system. Moreover, if a correct process delivers a message, then every correct process that has not expressed its will to leave the system delivers that message. We assume that more than $2/3$ of processes in the system are correct at all times, which is tight in our context. We also show that if only one process in the system can fail---and it can fail only by crashing---then it is impossible to implement a stronger primitive, ensuring that if any correct process in the system broadcasts or delivers a message, then every correct process in the system delivers that message---including those that leave., Comment: This is an extended version of a conference article, appearingin the proceedings of the 24th Int. Conference on Principles of Distributed Systems (OPODIS 2020). This work has been supported in part by a grant from Interchain Foundation

Online social networks have become a crucial medium to disseminate the latest political, commercial, and social information. Users with high visibility are often selected as seeds to spread information and affect their adoption in target groups. We study how gender differences and similarities can impact the information spreading process. Using a large-scale Instagram dataset and a small-scale Facebook dataset, we first conduct a multi-faceted analysis taking the interaction type, directionality and frequency into account. To this end, we explore a variety of existing and new single and multihop centrality measures. Our analysis unveils that males and females interact differently depending on the interaction types, e.g., likes or comments, and they feature different support and promotion patterns. We complement prior work showing that females do not reach top visibility (often referred to as the glass ceiling effect) jointly factoring in the connectivity and interaction intensity, both of which were previously mainly discussed independently. Inspired by these observations, we propose a novel seeding framework, called Disparity Seeding, which aims at maximizing spread while reaching a target user group, e.g., a certain percentage of females -- promoting the influence of under-represented groups. Disparity Seeding ranks influential users with two gender-aware measures, the Target HI-index and the Embedding index. Extensive simulations comparing Disparity Seeding with target-agnostic algorithms show that Disparity Seeding meets the target percentage while effectively maximizing the spread. Disparity Seeding can be generalized to counter different types of inequality, e.g., race, and proactively promote minorities in the society.

In many societies there is an elite, a relatively small group of powerful individuals that is well-connected and highly influential. Since the ancient days of Julius Caesar's senate of Rome to the recent days of celebrities on Twitter, the size of the elite is a result of conflicting social forces competing to increase or decrease it. The main contribution of this paper is the answer to the question how large the elite is at equilibrium. We take an axiomatic approach to solve this: assuming that an elite exists and it is influential, stable and either minimal or dense, we prove that its size must be $\Theta(\sqrt{m})$ (where $m$ is the number of edges in the network). As an approximation for the elite, we then present an empirical study on nine large real-world networks of the subgraph formed by the highest degree nodes, also known as the rich-club. Our findings indicate that elite properties such as disproportionate influence, stability and density of $\Theta(\sqrt{m})$-rich-clubs are universal properties and should join a growing list of common phenomena shared by social networks and complex systems such as "small world," power law degree distributions, high clustering, etc., Comment: under submission

The failure detector approach for solving distributed computing problems has been celebrated for its modularity. This approach allows the construction of algorithms using abstract failure detection mechanisms, defined by axiomatic properties, as building blocks. The minimal synchrony assumptions on communication, which enable to implement the failure detection mechanism, are studied separately. Such synchrony assumptions are typically expressed as eventual guarantees that need to hold, after some point in time, forever and deterministically. But in practice, they never do. Synchrony assumptions may hold only probabilistically and temporarily. In this paper, we study failure detectors in a realistic distributed system N, with asynchrony inflicted by probabilistic synchronous communication. We address the following paradox: an implementation of "consensus with probability 1" is possible in N without using randomness in the algorithm itself, while an implementation of "lozenge S with probability 1" is impossible to achieve in N (lozenge S being the weakest failure detector to solve the consensus problem and many equivalent problems). We circumvent this paradox by introducing a new failure detector lozenge S*, a variant of lozenge S with probabilistic and temporal accuracy. We prove that lozenge S* is implementable in N and we provide an optimal lozenge S* algorithm. Interestingly, we show that lozenge S* can replace lozenge S, in several existing deterministic consensus algorithms using lozenge S, to yield an algorithm that solves "consensus with probability 1". In fact, we show that such result holds for all decisive problems (not only consensus) and also for failure detector lozenge P (not only lozenge S). The resulting algorithms combine the modularity of distributed computing practices with the practicality of networking ones.