Investigation of the robustness of star graph networks

The star interconnection network has been known as an attractive alternative to n-cube for interconnecting a large number of processors. It possesses many nice properties, such as vertex/edge symmetry, recursiveness, sublogarithmic degree and diameter, and maximal fault tolerance, which are all desirable when building an interconnection topology for a parallel and distributed system. Investigation of the robustness of the star network architecture is essential since the star network has the potential of use in critical applications. In this study, three different reliability measures are proposed to investigate the robustness of the star network. First, a constrained two-terminal reliability measure referred to as Distance Reliability (DR) between the source node u and the destination node I with the shortest distance, in an n-dimensional star network, Sn, is introduced to assess the robustness of the star network. A combinatorial analysis on DR especially for u having a single cycle is performed under different failure models (node, link, combined node/link failure). Lower bounds on the special case of the DR: antipode reliability, are derived, compared with n-cube, and shown to be more fault-tolerant than n-cube. The degradation of a container in a Sn having at least one operational optimal path between u and I is also examined to measure the system effectiveness in the presence of failures under different failure models. The values of MTTF to each transition state are calculated and compared with similar size containers in n-cube. Meanwhile, an upper bound under the probability fault model and an approximation under the fixed partitioning approach on the ( n-1)-star reliability are derived, and proved to be similarly accurate and close to the simulations results. Conservative comparisons between similar size star networks and n-cubes show that the star network is more robust than n-cube in terms of ( n-1)-network reliability

On strong fault tolerance (or strong Menger-connectivity) of multicomputer networks

As the size of networks increases continuously, dealing with networks with faulty nodes becomes unavoidable. In this dissertation, we introduce a new measure for network fault tolerance, the strong fault tolerance (or strong Menger-connectivity)in multicomputer networks, and study the strong fault tolerance for popular multicomputer network structures. Let G be a network in which all nodes have degree d. We say that G is strongly fault tolerant if it has the following property: Let Gf be a copy of G with at most d - 2 faulty nodes. Then for any pair of non-faulty nodes u and v in Gf , there are min{degf (u), degf (v)} node-disjoint paths in Gf from u to v, where degf (u) and degf (v) are the degrees of the nodes u and v in Gf, respectively. First we study the strong fault tolerance for the popular network structures such as star networks and hypercube networks. We show that the star networks and the hypercube networks are strongly fault tolerant and develop efficient algorithms that construct the maximum number of node-disjoint paths of nearly optimal or optimal length in these networks when they contain faulty nodes. Our algorithms are optimal in terms of their time complexity. In addition to studying the strong fault tolerance, we also investigate a more realistic concept to describe the ability of networks for tolerating faults. The traditional definition of fault tolerance, sustaining at most d - 1faulty nodes for a regular graph G of degree d, reflects a very rare situation. In many cases, there is a chance that a routing path between two given nodes can be constructed though the network may have more faulty nodes than its degree. In this dissertation, we study the fault tolerance of hypercube networks under a probability model. When each node of the n-dimensional hypercube network has an independent failure probability p, we develop algorithms that, with very high probability, can construct a fault-free path when the hypercube network can sustain up to 2np faulty nodes

A study of SPRT algorithm and New-Guard for radiation detection

A novel and efficient radiation detection algorithm combined with a measuring unit will produce an ideal detector to battle field radiation measurement problems. Studies of Sequential Probability Ratio Test (SPRT) for radiation detection are essential towards developing efficient and accurate radiation detection algorithms. In this study, the performance of the classical Single-Threshold-Test (STT) and the SPRT First-In-First-Out (FIFO) algorithms is considered. Next, improvements made by the Last-In-First-Elected-Last-Out (LIFELO) algorithm are analyzed. Further, enhancements to the LIFELO algorithm, using the Dynamic Background Updating and Maximum Likelihood Estimator (MLE), are performed; The thesis also provides detailed requirements for an innovative hand-held radiation detection system and underlines additional features available on a New Generation User Adaptable Radiation Detector (New-GUARD) to help the field survey processes. Currently available technologies are studied to rationalize the need for the New-GUARD prototype. The New-GUARD is compared to similar products that are already available in the market to show its completeness as a radiation detector incorporated with Global Positioning System (GPS), wireless communication, and a self-correcting system. Primary performance evaluations of the algorithms are executed using Mathematica and further analysis is carried out with Matlab and C

The Effect of node Failures in Substar Reliability of a Star network- a Combinatorial Approach

The star graph is a hierarchical graph, and rich in containing substars (or graphs with smaller size but with the same topological properties as the original). Given a set of faulty nodes, we determine the ability to recover substars of a given dimension from the original network. A study of the number of faulty nodes that are required to damage every subnetwork of a given size is also presented