The paper proves some topological properties of bitonic sorters, which have found applications in constructing, along with banyan networks, internally nonblocking switching fabrics in future broadband networks. The states of all the sorting elements of an N/spl times/N bitonic sorter are studied for four different input sequences {a/sub i/}/sub i=l//sup N/, {b/sub i/}/sub i=l//sup N/, {c/sub i/}/sub i=l//sup N/, and {d/sub i/}/sub i=l//sup N/ where a/sub i/=i-1, b/sub i/=N-i, and the binary representations of c/sub i/ and d/sub i/ are the bit reverse of those of a/sub i/ and b/sub i/, respectively. An application of these topological properties is to help design efficient fault diagnosis procedures. We present an example for detecting and locating a single faulty sorting element under a simple fault model where all sorting elements are always in the straight state or the cross state.

Bitonic sorters have recently been proposed to construct along with banyan networks the switching fabric of future broadband networks. Unfortunately, a single fault in a bitonic sorter may have disastrous consequences for the switching system. Therefore, a bitonic sorter must be proved to be free of faults before it can be used. We study the topological properties of bitonic sorters and present an efficient fault diagnosis procedure to detect, locate, and identify the fault type of single faults. Our diagnosis procedure can detect most single faults in two tests. Faults which cannot be detected in two tests can always be detected in four tests. Several binary search techniques are developed to locate a faulty sorting element (i.e. a 2/spl times/2 sorter).>

The banyan network, and networks topologically equivalent to it, have recently been adopted as interconnection networks in multiprocessor systems. Often, a multiprocessor system is reconfigured when the banyan network becomes faulty. It is possible to avoid a complicated reconfiguration process as long as the faulty banyan network still possesses the dynamic full access (DFA) property. In this paper, we determine a necessary and sufficient condition for a faulty banyan network to possess the DFA property and design a test procedure based on the condition. The test procedure can be used to decompose a faulty banyan network into subsystems possessing the DFA property. We also evaluate the probability that a banyan network loses the DFA property, given the number of faulty switching elements. It is found that as long as faults do not occur in switching elements located in the first and last stages, this probability is very small, even when there are quite a few faulty switching elements.>

In order to utilize multiple-pass routing schemes, a faulty banyan network must possess the dynamic full access (DFA) property. The authors determine a necessary and sufficient condition for a banyan network to possess the DFA property and design a general testing procedure based on the condition. They also enumerate the probability that a banyan network loses the DFA property, given the number of faulty switch elements. It is found that, as long as faults do not occur in switch elements located in the first and last stages, this probability is very small even when there are quite a few faulty switch elements. Therefore, multiple-pass routing schemes can be very useful if the switch elements in the first and last stages are well protected.>