Two-Pass Rearrangeability in Faulty Benes Networks

doi:10.1006/jpdc.1996.0080

Journal of Parallel and Distributed Computing

Volume 35, Issue 2, 15 June 1996, Pages 191-198

https://doi.org/10.1006/jpdc.1996.0080 Get rights and content

Abstract

Existing fault-tolerant routing schemes for Benes networks either consider only the control line stuck-at faults, or handle the switch faults by some graceful degradation routing schemes that reconfigure the network into a smaller system with minimal loss. Now, even in the presence of a single switch fault in anN×NBenes networkB(n), (n= log₂N), noN×Npermutation can be realized in a single pass. In this paper, we attempt to characterize the switch fault sets inB(n), in the presence of which the network is always capable of realizing any arbitraryN×NpermutationPin two passes, such that any source–destination path is set up in a single pass, no recirculation is needed, but the whole set ofNsource–destination paths ofPis partitioned in two subsets and are realized in two successive passes. We propose an algorithm that will detect if the switch fault set present in aB(n), belongs to this class; if it is yes, we present another algorithm that computes the fault-tolerant routing to realize any arbitrary permutationPin two passes. This scheme enables us to makeB(n) fault-tolerant in the presence of a restricted class of multiple switch faults, without any recirculation through intermediate nodes, or any reconfiguration of the system.

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Cited by (2)

O (log m.log N) routing algorithm for (2log N-1) -stage switching networks and beyond
2014, Journal of Parallel and Distributed Computing
This paper addresses routing algorithm for a classic network called rearrangeable network with a complexity which is minimum than any other reported algorithms in this class. A new routing algorithm is presented for symmetric rearrangeable networks built with $2 \times 2$ switching elements. This new algorithm is capable of connection setup for partial permutation, $\bar{m} = ρ N$ , where $N$ is the total input numbers and $\bar{m}$ is the number of active inputs. Overall the serial time complexity of this method is $O (N \log N)$ ¹ and $O (\bar{m} . \log N)$ where all $N$ inputs are active and with $\bar{m} < N$ active inputs respectively. The time complexity of this algorithm in a parallel machine with $N$ completely connected processors is $O (\log^{2} N)$ . With $\bar{m}$ active requests the time complexity goes down to $O (\log \bar{m} . \log N)$ , which is better than the $O (\log^{2} \bar{m} + \log N)$ , reported in the literature for $2^{\frac{1}{2} [{(\log^{2} N - 4 \log N)}^{\frac{1}{2}} - \log N]} \leq ρ \leq 1$ . In later half of this paper, modified rearrangeable networks have been demonstrated built with bigger switching elements ( $> 2 \times 2$ ) with shorter network depth. Routing algorithm for these new networks have been proposed by modifying the proposed algorithm for smaller switching elements networks. Also we shall look into the application of these networks in optical domain for crosstalk free routing.
Low complexity routing algorithm for rearrangeable switching networks
2013, Proceedings - International Conference on Advanced Information Networking and Applications, AINA

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Research NoteTwo-Pass Rearrangeability in Faulty Benes Networks

Abstract

Research Note
Two-Pass Rearrangeability in Faulty Benes Networks