Efficient Bayesian Learning in Social Networks with Gaussian Estimators

We consider a group of Bayesian agents who try to estimate a state of the world $\theta$ through interaction on a social network. Each agent $v$ initially receives a private measurement of $\theta$: a number $S_v$ picked from a Gaussian distribution with mean $\theta$ and standard deviation one. Then, in each discrete time iteration, each reveals its estimate of $\theta$ to its neighbors, and, observing its neighbors' actions, updates its belief using Bayes' Law. This process aggregates information efficiently, in the sense that all the agents converge to the belief that they would have, had they access to all the private measurements. We show that this process is computationally efficient, so that each agent's calculation can be easily carried out. We also show that on any graph the process converges after at most $2N \cdot D$ steps, where $N$ is the number of agents and $D$ is the diameter of the network. Finally, we show that on trees and on distance transitive-graphs the process converges after $D$ steps, and that it preserves privacy, so that agents learn very little about the private signal of most other agents, despite the efficient aggregation of information. Our results extend those in an unpublished manuscript of the first and last authors.Comment: Added coauthor. Added proofs for fast convergence on trees and distance transitive graphs. Also, now analyzing a notion of privac

Investigation of reduced hypercube (RH) networks : embedding and routing capabilities

The choice of a topology for the interconnection of resources in a distributed-memory parallel computing system is a major design decision. The direct binary hypercube has been widely used for this purpose due to its low diameter and its ability to efficiently emulate other important structures. The aforementioned strong properties of the hypercube come at the cost of high VLSI complexity due to the increase in the number of communication ports and channels per node with an increase in the total number of nodes. The reduced hypercube (RH) topology, which is obtained by a uniform reduction in the number of links for each hypercube node, yields lower complexity interconnection networks compared to hypercubes with the same number of nodes, thus permitting the construction of larger parallel systems. Furthermore, it has been shown that the RH at a lower cost achieves performance comparable to that of a regular hypercube with the same number of nodes. A very important issue for the viability of the RH is to investigate the efficiency of embedding frequently used topologies into it. This thesis proposes embedding algorithms for three very important topologies, namely the ring, the torus and the binary tree. The performance of the proposed algorithms is analyzed and compared to that of equivalent embedding algorithms for the regular hypercube. It is shown that these topologies are emulated efficiently on the RH. Additionally, two already proposed routing algorithms for the RH are evaluated through simulation results

A novel QoS multicast model in mobile ad hoc networks

2004-2005 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe