Fault tolerance in a class of sorting networks
- Proocol Standards and Communications Inc., Ottawa, Ontario (Canada)
The early study of fault tolerance in efficient sorting networks only achieved single-fault tolerance. By eliminating critical comparators, Rudolph presented a 1-fault tolerant design of the balanced sorting network (BSN) at the cost of one redundant stage of N/2 comparators and two permuters external to the network. In this paper, we show, however, that 1-fault tolerance of BSN can be achieved without introducing redundancy and external permuters. Furthermore, we provide solutions to the open question of how to achieve multiple-fault tolerance in BSN. We analyze the problem from a higher-level by introducing a new concept of critical stages, and find that all stages in previous designs are critical. A 2-fault tolerant design of BSN is then discovered after eliminating its critical stages. The new design has a similar network architecture (i.e., a multistage network with the output recirculated back to the input) and the same hardware cost as Rudolph`s, but it has many distinguished features. (1) It becomes 3-fault tolerant by duplicating the redundant stage. (2) It can be generalized to a (k + 1)-fault tolerant design if 1greater than or = k redundant stages are added; and the resulting network has no critical stages but critical (k + 1)-tuples of stages. Sorting would fail if and only if all stages of a critical (k + 1)-tuple are faulty. (3) It can be extended to new topologies with an arbitrary number of stages, without external permuters, that may achieve an arbitrary degree of fault tolerance. The performance analysis shows that the new designs achieve much higher probabilities of correct sorting in the presence of faulty comparators than the previous reported designs. 21 refs.
- OSTI ID:
- 135325
- Journal Information:
- IEEE Transactions on Computers, Vol. 43, Issue 7; Other Information: PBD: Jul 1994
- Country of Publication:
- United States
- Language:
- English
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