The Power of Two Choices in Distributed Voting

Distributed voting is a fundamental topic in distributed computing. In pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts its opinion. The voting is completed when all vertices hold the same opinion. On many graph classes including regular graphs, pull voting requires $\Theta(n)$ expected steps to complete, even if initially there are only two distinct opinions. In this paper we consider a related process which we call two-sample voting: every vertex chooses two random neighbours in each step. If the opinions of these neighbours coincide, then the vertex revises its opinion according to the chosen sample. Otherwise, it keeps its own opinion. We consider the performance of this process in the case where two different opinions reside on vertices of some (arbitrary) sets $A$ and $B$, respectively. Here, $|A| + |B| = n$ is the number of vertices of the graph. We show that there is a constant $K$ such that if the initial imbalance between the two opinions is ?$\nu_0 = (|A| - |B|)/n \geq K \sqrt{(1/d) + (d/n)}$, then with high probability two sample voting completes in a random $d$ regular graph in $O(\log n)$ steps and the initial majority opinion wins. We also show the same performance for any regular graph, if $\nu_0 \geq K \lambda_2$ where $\lambda_2$ is the second largest eigenvalue of the transition matrix. In the graphs we consider, standard pull voting requires $\Omega(n)$ steps, and the minority can still win with probability $|B|/n$.Comment: 22 page

Rational Fair Consensus in the GOSSIP Model

The \emph{rational fair consensus problem} can be informally defined as follows. Consider a network of $n$ (selfish) \emph{rational agents}, each of them initially supporting a \emph{color} chosen from a finite set $\Sigma$. The goal is to design a protocol that leads the network to a stable monochromatic configuration (i.e. a consensus) such that the probability that the winning color is $c$ is equal to the fraction of the agents that initially support $c$, for any $c \in \Sigma$. Furthermore, this fairness property must be guaranteed (with high probability) even in presence of any fixed \emph{coalition} of rational agents that may deviate from the protocol in order to increase the winning probability of their supported colors. A protocol having this property, in presence of coalitions of size at most $t$, is said to be a \emph{whp\,-$t$-strong equilibrium}. We investigate, for the first time, the rational fair consensus problem in the GOSSIP communication model where, at every round, every agent can actively contact at most one neighbor via a \emph{push$/$pull} operation. We provide a randomized GOSSIP protocol that, starting from any initial color configuration of the complete graph, achieves rational fair consensus within $O(\log n)$ rounds using messages of $O(\log^2n)$ size, w.h.p. More in details, we prove that our protocol is a whp\,-$t$-strong equilibrium for any $t = o(n/\log n)$ and, moreover, it tolerates worst-case permanent faults provided that the number of non-faulty agents is $\Omega(n)$. As far as we know, our protocol is the first solution which avoids any all-to-all communication, thus resulting in $o(n^2)$ message complexity.Comment: Accepted at IPDPS'1

Distributed anonymous function computation in information fusion and multiagent systems

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we exhibit a class of non-computable functions, and prove that every function outside this class can at least be approximated. The problem of computing averages in a distributed manner plays a central role in our development

Local majorities, coalitions and monopolies in graphs: a review

AbstractThis paper provides an overview of recent developments concerning the process of local majority voting in graphs, and its basic properties, from graph theoretic and algorithmic standpoints

Bounds on the Voter Model in Dynamic Networks

In the voter model, each node of a graph has an opinion, and in every round each node chooses independently a random neighbour and adopts its opinion. We are interested in the consensus time, which is the first point in time where all nodes have the same opinion. We consider dynamic graphs in which the edges are rewired in every round (by an adversary) giving rise to the graph sequence $G_1, G_2, \dots$, where we assume that $G_i$ has conductance at least $\phi_i$. We assume that the degrees of nodes don't change over time as one can show that the consensus time can become super-exponential otherwise. In the case of a sequence of $d$-regular graphs, we obtain asymptotically tight results. Even for some static graphs, such as the cycle, our results improve the state of the art. Here we show that the expected number of rounds until all nodes have the same opinion is bounded by $O(m/(d_{min} \cdot \phi))$, for any graph with $m$ edges, conductance $\phi$, and degrees at least $d_{min}$. In addition, we consider a biased dynamic voter model, where each opinion $i$ is associated with a probability $P_i$, and when a node chooses a neighbour with that opinion, it adopts opinion $i$ with probability $P_i$ (otherwise the node keeps its current opinion). We show for any regular dynamic graph, that if there is an $\epsilon>0$ difference between the highest and second highest opinion probabilities, and at least $\Omega(\log n)$ nodes have initially the opinion with the highest probability, then all nodes adopt w.h.p. that opinion. We obtain a bound on the convergences time, which becomes $O(\log n/\phi)$ for static graphs

Analyses of Methods for Prediction of Elections Using Software Systems

The primary objective of this research study is to review and analyze the published literature regarding the possibilities of forecasting and predicting the result of elections using software systems. The factors motivating research institutions and individuals to consider research impact on prediction of elections are manifold. Understanding the impact of different software tools, algorithms and social networking software applications on prediction of elections is a vital, and often overlooked, element of forecasting the election results. The literature review was conducted to examine methods and current software applications and practices as well as projects on election predictions. The review focused in particular on social media applications and different methods on accessing the opinion of the potential voters. The review draws on an international literature, although it is limited to English language publications. The findings identify the different methods used, the advantages and disadvantages of different approaches and the methods that are used currently and that have shown most effective results and recommendations are provided

State of the art 2015: a literature review of social media intelligence capabilities for counter-terrorism

Overview This paper is a review of how information and insight can be drawn from open social media sources. It focuses on the specific research techniques that have emerged, the capabilities they provide, the possible insights they offer, and the ethical and legal questions they raise. These techniques are considered relevant and valuable in so far as they can help to maintain public safety by preventing terrorism, preparing for it, protecting the public from it and pursuing its perpetrators. The report also considers how far this can be achieved against the backdrop of radically changing technology and public attitudes towards surveillance. This is an updated version of a 2013 report paper on the same subject, State of the Art. Since 2013, there have been significant changes in social media, how it is used by terrorist groups, and the methods being developed to make sense of it.  The paper is structured as follows: Part 1 is an overview of social media use, focused on how it is used by groups of interest to those involved in counter-terrorism. This includes new sections on trends of social media platforms; and a new section on Islamic State (IS). Part 2 provides an introduction to the key approaches of social media intelligence (henceforth ‘SOCMINT’) for counter-terrorism. Part 3 sets out a series of SOCMINT techniques. For each technique a series of capabilities and insights are considered, the validity and reliability of the method is considered, and how they might be applied to counter-terrorism work explored. Part 4 outlines a number of important legal, ethical and practical considerations when undertaking SOCMINT work