Interconnection Networks Based on Gaussian and Eisenstein-Jacobi Integers

Quotient rings of Gaussian and Eisenstein-Jacobi(EJ) integers can be deployed to construct interconnection networks with good topological properties. In this thesis, we propose deadlock-free deterministic and partially adaptive routing algo­rithms for hexagonal networks, one special class of EJ networks. Then we discuss higher dimensional Gaussian networks as an alternative to classical multidimen­sional toroidal networks. For this topology, we explore many properties including distance distribution and the decomposition of higher dimensional Gaussian net­ works into Hamiltonian cycles. In addition, we propose some efficient communi­cation algorithms for higher dimensional Gaussian networks including one-to-all broadcasting and shortest path routing. Simulation results show that the rout­ing algorithm proposed for higher dimensional Gaussian networks outperforms the routing algorithm of the corresponding torus networks with approximately the same number of nodes. These simulation results are expected since higher dimen­sional Gaussian networks have a smaller diameter and a smaller average message latency as compared with toroidal networks. Finally, we introduce a degree-three interconnection network obtained from pruning a Gaussian network. This network shows possible performance improve­ment over other degree-three networks since it has a smaller diameter compared to other degree-three networks. Many topological properties of degree-three pruned Gaussian network are explored. In addition, an optimal shortest path routing algorithm and a one-to-all broadcasting algorithm are given

Mean field inference in dependency networks: An empirical study

Dependency networks are a compelling alternative to Bayesian networks for learning joint probability distributions from data and using them to compute probabilities. A dependency network consists of a set of conditional probability distributions, each representing the probability of a single variable given its Markov blanket. Running Gibbs sampling with these conditional distributions produces a joint distribution that can be used to answer queries, but suffers from the traditional slowness of sampling-based inference. In this paper, we observe that the mean field update equation can be applied to dependency networks, even though the conditional probability distributions may be inconsistent with each other. In experiments with learning and inference on 12 datasets, we demonstrate that mean field inference in dependency networks offers similar accuracy to Gibbs sampling but with orders of magnitude improvements in speed. Compared to Bayesian networks learned on the same data, dependency networks offer higher accuracy at greater amounts of evidence. Furthermore, mean field inference is consistently more accurate in dependency networks than in Bayesian networks learned on the same data

Improving a Fault-Tolerant Routing Algorithm Using Detailed Traffic Analysis

Abstract. Currently, some coarse measures like global network latency are used to compare routing protocols. These measures do not provide enough insight of traffic distribution among network nodes in presence of different fault regions. This paper presents a detailed traffic analysis of f-cube routing algorithm achieved by a especially developed tool. Per-node traffic analysis illustrates the traffic hotspots caused by fault regions and provides a great assistance in developing fault tolerant routing algorithms. Based on such detailed information, a simple yet effective improvement of f-cube is suggested. Moreover, the effect of a traffic hotspot on the traffic of neighboring nodes and global performance degradation is investigated. To analyze the per-node traffic, some per-node traffic metrics are introduced and one of them is selected for the rest of work. In an effort to gain deep understanding of the issue of traffic analysis of faulty networks, this paper is the first attempt to investigate per-node traffic around fault regions.