Subcube embeddability and fault tolerance of augmented hypercubes

Hypercube networks have received much attention from both parallel processing and communications areas over the years since they offer a rich interconnection structure with high bandwidth, logarithmic diameter, and high degree of fault tolerance. They are easily partitionable and exhibit a high degree of fault tolerance. Fault-tolerance in hypercube and hypercube-based networks received the attention of several researchers in recent years; The primary idea of this study is to address and analyze the reliability issues in hypercube networks. It is well known that the hypercube can be augmented with one dimension to replace any of the existing dimensions should any dimension fail. In this research, it is shown that it is possible to add i dimensions to the standard hypercube, Qn to tolerate (i - 1) dimension failures, where 0 \u3c i ≤ n. An augmented hypercube, Qn +(n) with n additional dimensions is introduced and compared with two other hypercube networks with the same amount of redundancy. Reliability analysis for the three hypercube networks is done using the combinatorial and Markov modeling. The MTTF values are calculated and compared for all three networks. Comparison between similar size hypercube networks show that the augmented hypercube is more robust than the standard hypercube; As a related problem, we also look at the subcube embeddability. Subcube embeddability of the hypercube can be enhanced by introducing an additional dimension. A set of new dimensions, characterized by the Hamming distance between the pairs of nodes it connects, is introduced using a measure defined as the magnitude of a dimension. An enumeration of subcubes of various sizes is presented for a dimension parameterized by its magnitude. It is shown that the maximum number of subcubes for a Qn can only be attained when the magnitude of dimension is n - 1 or n. It is further shown that the latter two dimensions can optimally increase the number of subcubes among all possible choices

An Adaptive Fault-Tolerant Communication Scheme for Body Sensor Networks

A high degree of reliability for critical data transmission is required in body sensor networks (BSNs). However, BSNs are usually vulnerable to channel impairments due to body fading effect and RF interference, which may potentially cause data transmission to be unreliable. In this paper, an adaptive and flexible fault-tolerant communication scheme for BSNs, namely AFTCS, is proposed. AFTCS adopts a channel bandwidth reservation strategy to provide reliable data transmission when channel impairments occur. In order to fulfill the reliability requirements of critical sensors, fault-tolerant priority and queue are employed to adaptively adjust the channel bandwidth allocation. Simulation results show that AFTCS can alleviate the effect of channel impairments, while yielding lower packet loss rate and latency for critical sensors at runtime.Comment: 10 figures, 19 page

Reliable fault-tolerant model predictive control of drinking water transport networks

This paper proposes a reliable fault-tolerant model predictive control applied to drinking water transport networks. After a fault has occurred, the predictive controller should be redesigned to cope with the fault effect. Before starting to apply the fault-tolerant control strategy, it should be evaluated whether the predictive controller will be able to continue operating after the fault appearance. This is done by means of a structural analysis to determine loss of controllability after the fault complemented with feasibility analysis of the optimization problem related to the predictive controller design, so as to consider the fault effect in actuator constraints. Moreover, by evaluating the admissibility of the different actuator-fault configurations, critical actuators regarding fault tolerance can be identified considering structural, feasibility, performance and reliability analyses. On the other hand, the proposed approach allows a degradation analysis of the system to be performed. As a result of these analyses, the predictive controller design can be modified by adapting constraints such that the best achievable performance with some pre-established level of reliability will be achieved. The proposed approach is tested on the Barcelona drinking water transport network.Postprint (author's final draft

On quantifying fault patterns of the mesh interconnect networks

One of the key issues in the design of Multiprocessors System-on-Chip (MP-SoCs), multicomputers, and peerto- peer networks is the development of an efficient communication network to provide high throughput and low latency and its ability to survive beyond the failure of individual components. Generally, the faulty components may be coalesced into fault regions, which are classified into convex and concave shapes. In this paper, we propose a mathematical solution for counting the number of common fault patterns in a 2-D mesh interconnect network including both convex (|-shape, | |-shape, ý-shape) and concave (L-shape, Ushape, T-shape, +-shape, H-shape) regions. The results presented in this paper which have been validated through simulation experiments can play a key role when studying, particularly, the performance analysis of fault-tolerant routing algorithms and measure of a network fault-tolerance expressed as the probability of a disconnection

Sparse Fault-Tolerant BFS Trees

This paper addresses the problem of designing a sparse {\em fault-tolerant} BFS tree, or {\em FT-BFS tree} for short, namely, a sparse subgraph $T$ of the given network $G$ such that subsequent to the failure of a single edge or vertex, the surviving part $T'$ of $T$ still contains a BFS spanning tree for (the surviving part of) $G$. Our main results are as follows. We present an algorithm that for every $n$-vertex graph $G$ and source node $s$ constructs a (single edge failure) FT-BFS tree rooted at $s$ with O(n \cdot \min\{\Depth(s), \sqrt{n}\}) edges, where \Depth(s) is the depth of the BFS tree rooted at $s$. This result is complemented by a matching lower bound, showing that there exist $n$-vertex graphs with a source node $s$ for which any edge (or vertex) FT-BFS tree rooted at $s$ has $\Omega(n^{3/2})$ edges. We then consider {\em fault-tolerant multi-source BFS trees}, or {\em FT-MBFS trees} for short, aiming to provide (following a failure) a BFS tree rooted at each source $s\in S$ for some subset of sources $S\subseteq V$. Again, tight bounds are provided, showing that there exists a poly-time algorithm that for every $n$-vertex graph and source set $S \subseteq V$ of size $\sigma$ constructs a (single failure) FT-MBFS tree $T^*(S)$ from each source $s_i \in S$, with $O(\sqrt{\sigma} \cdot n^{3/2})$ edges, and on the other hand there exist $n$-vertex graphs with source sets $S \subseteq V$ of cardinality $\sigma$, on which any FT-MBFS tree from $S$ has $\Omega(\sqrt{\sigma}\cdot n^{3/2})$ edges. Finally, we propose an $O(\log n)$ approximation algorithm for constructing FT-BFS and FT-MBFS structures. The latter is complemented by a hardness result stating that there exists no $\Omega(\log n)$ approximation algorithm for these problems under standard complexity assumptions

Resilient Quantum Computation: Error Models and Thresholds

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error-correction, fault tolerant state recovery, fault tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.Comment: 19 pages in RevTex, many figures, the paper is also avalaible at http://qso.lanl.gov/qc