Mutual test and diagnosis: architectures and algorithms for spacecraft avionics

LaForge, L.E.; Korver, K.F.

doi:10.1109/aero.2000.878501

Cited by 5 publications

(3 citation statements)

References 22 publications

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“…To focus on architectures we make three simplifying assumptions: i) faults have been correctly diagnosed [27], [29]; ii) the outcome of this diagnosis is passed to an algorithm that effects the configuration; iii) only vertices (and not edges) may be deleted. Assumptions (i) and (ii) are substantive issues, and are addressed in some detail by [25].…”

Section: Taxonomy Of Graph Architecturesmentioning

confidence: 99%

What designers of bus and network architectures should know about hypercubes

LaForge¹,

Korver²,

Fadali³

2003

IEEE Trans. Comput.

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We quantify why, as designers, we should prefer clique-based hypercubes (K-cubes) over traditional hypercubes based on cycles (C-cubes). Reaping fresh analytic results, we find that K-cubes minimize the wirecount and, simultaneously, the latency of hypercube architectures that tolerate failure of any f nodes. Refining the graph model of Hayes (1976), we pose the feasibility of configuration as a problem in multivariate optimization: What (f +1)-connected n-vertex graphs with fewest edges n(f+1)/2 minimize the maximum a) radius or b) diameter of subgraphs (i.e., quorums) induced by deleting up to f vertices? (1) We solve (1) for f that is superlogarithmic but sublinear in n, and in the process prove: I) the fault tolerance of K-cubes is proportionally greater than that of C-cubes; II) quorums formed from K-cubes have a diameter that is asymptotically convergent to the Moore Bound on radius; III) under any conditions of scaling, by contrast, C-cubes diverge from the Moore Bound. Thus, K-cubes are optimal, while C-cubes are suboptimal. Our exposition furthermore: IV) counterexamples, corrects, and generalizes a mistaken claim by Armstrong and Gray (1981) concerning binary cubes; V) proves that K-cubes and certain of their quorums are the only graphs which can be labeled such that the edge distance between any two vertices equals the Hamming distance between their labels; and VI) extends our results to K-cube-connected cycles and edges. We illustrate and motivate our work with applications to the synthesis of multicomputer architectures for deep space missions.

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Section: Taxonomy Of Graph Architecturesmentioning

confidence: 99%

What designers of bus and network architectures should know about hypercubes

LaForge¹,

Korver²,

Fadali³

2003

IEEE Trans. Comput.

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“…Such a test MUTEX calls for (weak) onefactorization of a test digraph D, akin to minimum-length schedules satisfying workloads for MANETs (5) and switch fabrics. But first, let's check that the number of tests in fact warrants the effort of minimum length scheduling.LaForge and Korver[41] underscore a remarkable coincidence: the test cost of MTAD is essentially the same as the channel cost of fault tolerance, as noted on page 5, and as plotted inFigures 7, 13a, and 13b of…”

mentioning

confidence: 85%

“…Perhaps the starkest distinction between random graphs and stochastic subgraphs arises with Blough's counterexample G B (n , p, h) to Scheinerman's claim that Ω(n log n) tests are necessary to almost surely diagnose faults distributed with Bernoulli probability p [6], [41], [54]. i.e., p < ½.…”

Section: A4 Probabilistically Tuned Fault Diagnosis and Tolerancementioning

confidence: 99%

Spaceflight Multi-Processors with Fault Tolerance and Connectivity Tuned from Sparse to Dense

LaForge¹,

Moreland²,

Fadali³

2006 IEEE Aerospace Conference

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A fault is a condition which renders the node or channel untrustworthy, hence (in this paper) unusable. A network instantaneously subjected to faulty nodes and channels tolerates them if the remaining healthy nodes and channels form a quorum. Also in this paper: we assume that faulty nodes have been diagnosed, and that hardware and software can deny their connection to healthy nodes. The fault tolerance is the maximum number of faults that an n-node network can tolerate. Under a graph model, the tolerance f to faulty nodes is at most the tolerance to faults in channels, or any combination of faults in nodes and channels, for n > f+1 > 1. Throughput this paper we therefore employ a conservative model of faults in nodes. The worst-case (nodal) network fault tolerance f equals one less than the (vertex) connectivity f+1 of the corresponding graph. The fractional fault tolerance f / n equals the fault tolerance divided by the number of nodes. The fractional connectivity ( f + 1) / n is only slightly less than the fractional fault tolerance, and is more convenient for comparing the cost of worst-case fault tolerance with the probabilistic cost of tolerating a constant fraction of faults that are distributed, say, with Bernoulli probability pdi)graph: directed, weighted Vertex, edge, arc, hyperedge: pp. 4, 5, 13. Planar: pp. 10, 14. Cf. adjacency. Strict graph: each edge's endpoints are distinct (no loops) and appear in but one edge. Cf. multi-graph p. 9 Hamiltonian; p. 8 Path or cycle spanning all vertices Hamming distance, graph Definitions: p. 13. Also see Gray code, p. 13 (hyper)cube; mesh Definitions: pp. 13, 20. Qualifiers: dimension, (majorized ) radix. Cf. hyperedge, j-edge. (hyper)edge, separator Definitions: pp. 13, 14. Also see: hyperedge matching, hyperfactorization, p. 14 interior-disjoint, IDJ; p. 5 Two paths are interior-disjoint ( IDJ ) if, apart from their endpoints, they do not intersect metric space, distance; distance space; Table 1 Real-valued distance |⋅, ⋅| ≥ 0 mapping all pairs from a given set, such that: a) |x, y| = 0 if and only if x = y; b) symmetry: |x, y| = |x, y|; c) triangle inequality: |x, y| ≤ |x, y| + |x, y| order, size; p. 10 Vertex resp. edge cardinality path, endpoint, (path)length; pp. 4, 17Endpoint vertex x, or union P(x … z) of path P(x … y) with edge ( y, z ), such that y and z ∉ P(x … y) are endpoints of P(x … y) resp. P(x … z). The (path)length of P is its size quorum; p. 4 A configuration of processing nodes capable of accomplishing the mission. A quorum is achieved if sufficient healthy nodes (i.e., nodes that have not failed) remain capable of communicating among themselves. In graph-theoretic terms, a quorum is equivalent to a connected subgraph (or component) induced by deleting, from the graph corresponding to the original network, vertices and edges corresponding to faulty nodes and channels. The basic idea of a quorum as a connected induced subgraph may be varied by imposing constraints (e.g., we could insist the quorum be a tree [30] or an array [36]), or by relaxing...

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Fault Diagnostics

2017

Integrated System Health Management

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Mutual test and diagnosis: architectures and algorithms for spacecraft avionics

Cited by 5 publications

References 22 publications

What designers of bus and network architectures should know about hypercubes

What designers of bus and network architectures should know about hypercubes

Spaceflight Multi-Processors with Fault Tolerance and Connectivity Tuned from Sparse to Dense

Fault Diagnostics

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