Fault-tolerant meshes with minimal numbers of spares

This paper presents several techniques for adding fault-tolerance to distributed memory parallel computers. More formally, given a target graph with n nodes, we create a fault-tolerant graph with n + k nodes such that given any set of k or fewer faulty nodes, the remaining graph is guaranteed to contain the target graph as a fault-free subgraph. As a result, any algorithm designed for the target graph will run with no slowdown in the presence of k or fewer node faults, regardless of their distribution. We present fault-tolerant graphs for target graphs which are 2-dimensional meshes, tori, eight-connected meshes and hexagonal meshes. In all cases our fault-tolerant graphs have smaller degree than any previously known graphs with the same properties

Fault-tolerant meshes and hypercubes with minimal numbers of spares

Many parallel computers consist of processors connected in the form of a d-dimensional mesh or hypercube. Two- and three-dimensional meshes have been shown to be efficient in manipulating images and dense matrices, whereas hypercubes have been shown to be well suited to divide-and-conquer algorithms requiring global communication. However, even a single faulty processor or communication link can seriously affect the performance of these machines. This paper presents several techniques for tolerating faults in d-dimensional mesh and hypercube architectures. Our approach consists of adding spare processors and communication links so that the resulting architecture will contain a fault-free mesh or hypercube in the presence of faults. We optimize the cost of the fault-tolerant architecture by adding exactly k spare processors (while tolerating up to k processor and/or link faults) and minimizing the maximum number of links per processor. For example, when the desired architecture is a d-dimensional mesh and k = 1, we present a fault-tolerant architecture that has the same maximum degree as the desired architecture (namely, 2d) and has only one spare processor. We also present efficient layouts for fault-tolerant two- and three-dimensional meshes, and show how multiplexers and buses can be used to reduce the degree of fault-tolerant architectures. Finally, we give constructions for fault-tolerant tori, eight-connected meshes, and hexagonal meshes

Various heuristic algorithms to minimise the two-page crossing numbers of graphs

We propose several new heuristics for the twopage book crossing problem, which are based on recent algorithms for the corresponding one-page problem. Especially, the neural network model for edge allocation is combined for the first time with various one-page algorithms. We investigate the performance of the new heuristics by testing them on various benchmark test suites. It is found out that the new heuristics outperform the previously known heuristics and produce good approximations of the planar crossing number for severalwell-known graph families. We conjecture that the optimal two-page drawing of a graph represents the planar drawing of the graph

Detailed Modeling and Reliability Analysis of Fault-Tolerant Processor Arrays

Recent advances in VLSI/WSI technology have led to the design of processor arrays with a large number of processing elements confined in small areas. The use of redundancy to increase fault-tolerance has the effect of reducing the ratio of area dedicated to processing elements over the area occupied by other resources in the array. The assumption of fault-free hardware support (switches, buses, interconnection links, etc.,), leads at best to conservative reliability estimates. However, detailed modeling entails not only an explosive growth in the model state space but also a difficult model construction process. To address the latter problem, a systematic method to construct Markov models for the reliability evaluation of processor arrays is proposed. This method is based on the premise that the fault behavior of a processor array can be modeled by a Stochastic Petri Net (SPN). However, in order to obtain a more compact representation, a set of attributes is associated with each transition in the Petri net model. This representation is referred to as a Modified Stochastic Petri Net (MSPN) model. A MSPN allows the construction of the corresponding Markov model as the reachability graph is being generated. The Markov model generated can include the effect of failures of several different components of the array as well as the effect of a peculiar distribution of faults when the reconfiguration occurs. Specific reconfiguration schemes such as Successive Row Elimination (SRE), Alternate Row-Column Elimination (ARCE) and Direct Reconfiguration (DR), are analyze

Reliable and Efficient Parallel Processing Algorithms and Architectures for Modern Signal Processing

Least-squares (LS) estimations and spectral decomposition algorithms constitute the heart of modern signal processing and communication problems. Implementations of recursive LS and spectral decomposition algorithms onto parallel processing architectures such as systolic arrays with efficient fault-tolerant schemes are the major concerns of this dissertation. There are four major results in this dissertation. First, we propose the systolic block Householder transformation with application to the recursive least-squares minimization. It is successfully implemented on a systolic array with a two-level pipelined implementation at the vector level as well as at the word level. Second, a real-time algorithm-based concurrent error detection scheme based on the residual method is proposed for the QRD RLS systolic array. The fault diagnosis, order degraded reconfiguration, and performance analysis are also considered. Third, the dynamic range, stability, error detection capability under finite-precision implementation, order degraded performance, and residual estimation under faulty situations for the QRD RLS systolic array are studied in details. Finally, we propose the use of multi-phase systolic algorithms for spectral decomposition based on the QR algorithm. Two systolic architectures, one based on triangular array and another based on rectangular array, are presented for the multiphase operations with fault-tolerant considerations. Eigenvectors and singular vectors can be easily obtained by using the multi-pase operations. Performance issues are also considered

Design Disjunction for Resilient Reconfigurable Hardware

Contemporary reconfigurable hardware devices have the capability to achieve high performance, power efficiency, and adaptability required to meet a wide range of design goals. With scaling challenges facing current complementary metal oxide semiconductor (CMOS), new concepts and methodologies supporting efficient adaptation to handle reliability issues are becoming increasingly prominent. Reconfigurable hardware and their ability to realize self-organization features are expected to play a key role in designing future dependable hardware architectures. However, the exponential increase in density and complexity of current commercial SRAM-based field-programmable gate arrays (FPGAs) has escalated the overhead associated with dynamic runtime design adaptation. Traditionally, static modular redundancy techniques are considered to surmount this limitation; however, they can incur substantial overheads in both area and power requirements. To achieve a better trade-off among performance, area, power, and reliability, this research proposes design-time approaches that enable fine selection of redundancy level based on target reliability goals and autonomous adaptation to runtime demands. To achieve this goal, three studies were conducted: First, a graph and set theoretic approach, named Hypergraph-Cover Diversity (HCD), is introduced as a preemptive design technique to shift the dominant costs of resiliency to design-time. In particular, union-free hypergraphs are exploited to partition the reconfigurable resources pool into highly separable subsets of resources, each of which can be utilized by the same synthesized application netlist. The diverse implementations provide reconfiguration-based resilience throughout the system lifetime while avoiding the significant overheads associated with runtime placement and routing phases. Evaluation on a Motion-JPEG image compression core using a Xilinx 7-series-based FPGA hardware platform has demonstrated the potential of the proposed FT method to achieve 37.5% area saving and up to 66% reduction in power consumption compared to the frequently-used TMR scheme while providing superior fault tolerance. Second, Design Disjunction based on non-adaptive group testing is developed to realize a low-overhead fault tolerant system capable of handling self-testing and self-recovery using runtime partial reconfiguration. Reconfiguration is guided by resource grouping procedures which employ non-linear measurements given by the constructive property of f-disjunctness to extend runtime resilience to a large fault space and realize a favorable range of tradeoffs. Disjunct designs are created using the mosaic convergence algorithm developed such that at least one configuration in the library evades any occurrence of up to d resource faults, where d is lower-bounded by f. Experimental results for a set of MCNC and ISCAS benchmarks have demonstrated f-diagnosability at the individual slice level with average isolation resolution of 96.4% (94.4%) for f=1 (f=2) while incurring an average critical path delay impact of only 1.49% and area cost roughly comparable to conventional 2-MR approaches. Finally, the proposed Design Disjunction method is evaluated as a design-time method to improve timing yield in the presence of large random within-die (WID) process variations for application with a moderately high production capacity