Pooling or sampling: Collective dynamics for electrical flow estimation

The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully decentralized way is implicit in a number of biological systems. Thus, a natural question is whether this task can provably be accomplished in an efficient way by a network of agents executing a simple protocol. We provide a positive answer, proposing two distributed approaches to electrical flow computation on a weighted network: a deterministic process mimicking Jacobi's iterative method for solving linear systems, and a randomized token diffusion process, based on revisiting a classical random walk process on a graph with an absorbing node. We show that both processes converge to a solution of Kirchhoff's node potential equations, derive bounds on their convergence rates in terms of the weights of the network, and analyze their time and message complexity

Experiments with the Traveler's Dilemma: Welfare, Strategic Choice and Implicit Collusion

This paper investigates behavior in the Traveler's Dilemma game and isolates deviations from textbook predictions caused by differences in welfare perceptions and strategic miscalculations. It presents the results of an experimental analysis based on a 2x2 design where the own and the other subject's bonus-penalty parameters are changed independently. We find that the change in own bonus-penalty alone entirely explains the effect on claims of a simultaneous change in one's own and the other's bonus-penalty. An increase in the other subject's bonus-penalty has a significant negative effect on claims when the own bonus-penalty is low, whereas it does not have a significant effect when the own bonus-penalty is high. We also find that expected claims are inconsistent with actual claims in the asymmetric treatments. Focusing on reported strategies, we document substantial heterogeneity and show that changes in choices across treatments are largely explained by risk aversion.

Stabilizing Consensus with Many Opinions

We consider the following distributed consensus problem: Each node in a complete communication network of size $n$ initially holds an \emph{opinion}, which is chosen arbitrarily from a finite set $\Sigma$. The system must converge toward a consensus state in which all, or almost all nodes, hold the same opinion. Moreover, this opinion should be \emph{valid}, i.e., it should be one among those initially present in the system. This condition should be met even in the presence of an adaptive, malicious adversary who can modify the opinions of a bounded number of nodes in every round. We consider the \emph{3-majority dynamics}: At every round, every node pulls the opinion from three random neighbors and sets his new opinion to the majority one (ties are broken arbitrarily). Let $k$ be the number of valid opinions. We show that, if $k \leqslant n^{\alpha}$, where $\alpha$ is a suitable positive constant, the 3-majority dynamics converges in time polynomial in $k$ and $\log n$ with high probability even in the presence of an adversary who can affect up to $o(\sqrt{n})$ nodes at each round. Previously, the convergence of the 3-majority protocol was known for $|\Sigma| = 2$ only, with an argument that is robust to adversarial errors. On the other hand, no anonymous, uniform-gossip protocol that is robust to adversarial errors was known for $|\Sigma| > 2$

Experiments with the Traveler's Dilemma: Welfare, Strategic Choice and Implicit Collusion

This paper investigates behavior in the Traveler's Dilemma game and isolates deviations from textbook predictions caused by di®erences in welfare perceptions and strategic miscalculations. It presents the results of an experimental analysis based on a 2x2 design where the own and the other subject's bonus-penalty parameters are changed independently. We ¯nd that the change in own bonus-penalty alone entirely explains the e®ect on claims of a simultaneous change in one's own and the other's bonus-penalty. An increase in the other subject's bonus-penalty has a signi¯cant negative e®ect on claims when the own bonus-penalty is low, whereas it does not have a signi¯cant e®ect when the own bonus-penalty is high. We also ¯nd that expected claims are inconsistent with actual claims in the asymmetric treatments. Focus- ing on reported strategies, we document substantial heterogeneity and show that changes in choices across treatments are to a large extent explained by risk aversion.

Fully decentralized computation of aggregates over data streams

In several emerging applications, data is collected in massive streams at several distributed points of observation. A basic and challenging task is to allow every node to monitor a neighbourhood of interest by issuing continuous aggregate queries on the streams observed in its vicinity. This class of algorithms is fully decentralized and diffusive in nature: collecting all data at few central nodes of the network is unfeasible in networks of low capability devices or in the presence of massive data sets. The main difficulty in designing diffusive algorithms is to cope with duplicate detections. These arise both from the observation of the same event at several nodes of the network and/or receipt of the same aggregated information along multiple paths of diffusion. In this paper, we consider fully decentralized algorithms that answer locally continuous aggregate queries on the number of distinct events, total number of events and the second frequency moment in the scenario outlined above. The proposed algorithms use in the worst case or on realistic distributions sublinear space at every node. We also propose strategies that minimize the communication needed to update the aggregates when new events are observed. We experimentally evaluate for the efficiency and accuracy of our algorithms on realistic simulated scenarios

Tour recommendation for groups

Consider a group of people who are visiting a major touristic city, such as NY, Paris, or Rome. It is reasonable to assume that each member of the group has his or her own interests or preferences about places to visit, which in general may differ from those of other members. Still, people almost always want to hang out together and so the following question naturally arises: What is the best tour that the group could perform together in the city? This problem underpins several challenges, ranging from understanding people’s expected attitudes towards potential points of interest, to modeling and providing good and viable solutions. Formulating this problem is challenging because of multiple competing objectives. For example, making the entire group as happy as possible in general conflicts with the objective that no member becomes disappointed. In this paper, we address the algorithmic implications of the above problem, by providing various formulations that take into account the overall group as well as the individual satisfaction and the length of the tour. We then study the computational complexity of these formulations, we provide effective and efficient practical algorithms, and, finally, we evaluate them on datasets constructed from real city data

Self-Stabilizing Repeated Balls-into-Bins

We study the following synchronous process that we call "repeated balls-into-bins". The process is started by assigning $n$ balls to $n$ bins in an arbitrary way. In every subsequent round, from each non-empty bin one ball is chosen according to some fixed strategy (random, FIFO, etc), and re-assigned to one of the $n$ bins uniformly at random. We define a configuration "legitimate" if its maximum load is $\mathcal{O}(\log n)$. We prove that, starting from any configuration, the process will converge to a legitimate configuration in linear time and then it will only take on legitimate configurations over a period of length bounded by any polynomial in $n$, with high probability (w.h.p.). This implies that the process is self-stabilizing and that every ball traverses all bins in $\mathcal{O}(n \log^2 n)$ rounds, w.h.p

Simple Dynamics for Plurality Consensus

We study a \emph{Plurality-Consensus} process in which each of $n$ anonymous agents of a communication network initially supports an opinion (a color chosen from a finite set $[k]$). Then, in every (synchronous) round, each agent can revise his color according to the opinions currently held by a random sample of his neighbors. It is assumed that the initial color configuration exhibits a sufficiently large \emph{bias} $s$ towards a fixed plurality color, that is, the number of nodes supporting the plurality color exceeds the number of nodes supporting any other color by $s$ additional nodes. The goal is having the process to converge to the \emph{stable} configuration in which all nodes support the initial plurality. We consider a basic model in which the network is a clique and the update rule (called here the \emph{3-majority dynamics}) of the process is the following: each agent looks at the colors of three random neighbors and then applies the majority rule (breaking ties uniformly). We prove that the process converges in time $\mathcal{O}( \min\{ k, (n/\log n)^{1/3} \} \, \log n )$ with high probability, provided that $s \geqslant c \sqrt{ \min\{ 2k, (n/\log n)^{1/3} \}\, n \log n}$. We then prove that our upper bound above is tight as long as $k \leqslant (n/\log n)^{1/4}$. This fact implies an exponential time-gap between the plurality-consensus process and the \emph{median} process studied by Doerr et al. in [ACM SPAA'11]. A natural question is whether looking at more (than three) random neighbors can significantly speed up the process. We provide a negative answer to this question: In particular, we show that samples of polylogarithmic size can speed up the process by a polylogarithmic factor only.Comment: Preprint of journal versio

Stochastic Query Covering for Fast Approximate Document Retrieval

We design algorithms that, given a collection of documents and a distribution over user queries, return a small subset of the document collection in such a way that we can efficiently provide high-quality answers to user queries using only the selected subset. This approach has applications when space is a constraint or when the query-processing time increases significantly with the size of the collection. We study our algorithms through the lens of stochastic analysis and prove that even though they use only a small fraction of the entire collection, they can provide answers to most user queries, achieving a performance close to the optimal. To complement our theoretical findings, we experimentally show the versatility of our approach by considering two important cases in the context of Web search. In the first case, we favor the retrieval of documents that are relevant to the query, whereas in the second case we aim for document diversification. Both the theoretical and the experimental analysis provide strong evidence of the potential value of query covering in diverse application scenarios