Finite-time Convergent Gossiping

Gossip algorithms are widely used in modern distributed systems, with applications ranging from sensor networks and peer-to-peer networks to mobile vehicle networks and social networks. A tremendous research effort has been devoted to analyzing and improving the asymptotic rate of convergence for gossip algorithms. In this work we study finite-time convergence of deterministic gossiping. We show that there exists a symmetric gossip algorithm that converges in finite time if and only if the number of network nodes is a power of two, while there always exists an asymmetric gossip algorithm with finite-time convergence, independent of the number of nodes. For $n=2^m$ nodes, we prove that a fastest convergence can be reached in $nm=n\log_2 n$ node updates via symmetric gossiping. On the other hand, under asymmetric gossip among $n=2^m+r$ nodes with $0\leq r<2^m$, it takes at least $mn+2r$ node updates for achieving finite-time convergence. It is also shown that the existence of finite-time convergent gossiping often imposes strong structural requirements on the underlying interaction graph. Finally, we apply our results to gossip algorithms in quantum networks, where the goal is to control the state of a quantum system via pairwise interactions. We show that finite-time convergence is never possible for such systems.Comment: IEEE/ACM Transactions on Networking, In Pres

Greedy Gossip with Eavesdropping

This paper presents greedy gossip with eavesdropping (GGE), a novel randomized gossip algorithm for distributed computation of the average consensus problem. In gossip algorithms, nodes in the network randomly communicate with their neighbors and exchange information iteratively. The algorithms are simple and decentralized, making them attractive for wireless network applications. In general, gossip algorithms are robust to unreliable wireless conditions and time varying network topologies. In this paper we introduce GGE and demonstrate that greedy updates lead to rapid convergence. We do not require nodes to have any location information. Instead, greedy updates are made possible by exploiting the broadcast nature of wireless communications. During the operation of GGE, when a node decides to gossip, instead of choosing one of its neighbors at random, it makes a greedy selection, choosing the node which has the value most different from its own. In order to make this selection, nodes need to know their neighbors' values. Therefore, we assume that all transmissions are wireless broadcasts and nodes keep track of their neighbors' values by eavesdropping on their communications. We show that the convergence of GGE is guaranteed for connected network topologies. We also study the rates of convergence and illustrate, through theoretical bounds and numerical simulations, that GGE consistently outperforms randomized gossip and performs comparably to geographic gossip on moderate-sized random geometric graph topologies.Comment: 25 pages, 7 figure

Exploiting Interference for Efficient Distributed Computation in Cluster-based Wireless Sensor Networks

This invited paper presents some novel ideas on how to enhance the performance of consensus algorithms in distributed wireless sensor networks, when communication costs are considered. Of particular interest are consensus algorithms that exploit the broadcast property of the wireless channel to boost the performance in terms of convergence speeds. To this end, we propose a novel clustering based consensus algorithm that exploits interference for computation, while reducing the energy consumption in the network. The resulting optimization problem is a semidefinite program, which can be solved offline prior to system startup.Comment: Accepted for publication at IEEE Global Conference on Signal and Information Processing (GlobalSIP 2013

On Endogenous Random Consensus and Averaging Dynamics

Motivated by various random variations of Hegselmann-Krause model for opinion dynamics and gossip algorithm in an endogenously changing environment, we propose a general framework for the study of endogenously varying random averaging dynamics, i.e.\ an averaging dynamics whose evolution suffers from history dependent sources of randomness. We show that under general assumptions on the averaging dynamics, such dynamics is convergent almost surely. We also determine the limiting behavior of such dynamics and show such dynamics admit infinitely many time-varying Lyapunov functions

Contour: A Practical System for Binary Transparency

Transparency is crucial in security-critical applications that rely on authoritative information, as it provides a robust mechanism for holding these authorities accountable for their actions. A number of solutions have emerged in recent years that provide transparency in the setting of certificate issuance, and Bitcoin provides an example of how to enforce transparency in a financial setting. In this work we shift to a new setting, the distribution of software package binaries, and present a system for so-called "binary transparency." Our solution, Contour, uses proactive methods for providing transparency, privacy, and availability, even in the face of persistent man-in-the-middle attacks. We also demonstrate, via benchmarks and a test deployment for the Debian software repository, that Contour is the only system for binary transparency that satisfies the efficiency and coordination requirements that would make it possible to deploy today.Comment: International Workshop on Cryptocurrencies and Blockchain Technology (CBT), 201