Abhijit Sengupta

On some topological properties of hypercube, incomplete hypercube and supercube

Hamiltonian properties of hypercube, incomplete hypercube and supercube are examined. It is known that in a nonfaulty hypercube there are at least n! Hamiltonian cycles. The authors extend this result showing that the lower bound is at least 2/sup n-3/n! They show that with at most n-2 faulty links a faulty hypercube has at least 2(n-2)! Hamiltonian cycles. They establish that an incomplete hypercube with odd (even) number of nodes has (n-2)! Hamiltonian paths (cycles). They show that a supercube has at least (n-1)! Hamiltonian cycles and when the number of nodes is 2/sup n-1/+2/sup n-2/, then the number of Hamiltonian cycles is at least as high as 2(n-1)!.<<ETX>>

Self-routing algorithms for strongly regular multistage interconnection networks

Abstract This paper presents a self-routing algorithm for a class of permutations that can be represented as linear transportations and complementations. This class includes bit-permute-complement (BPC) [6] and several of other frequently used permutations. The same problem for a Benes or a shuffle-exchange network was considered earlier by Boppana and Raghavendra. This paper considers a more general problem by considering a broader class of multistage interconnection networks that includes these networks along with variety of others. For this class of interconnection networks, Nassimi presented a routing algorithm for BPC class. In effect, this paper considers the problem of routing a larger class of permutations than that considered by Nassimi for a broader class of networks than that considered by Boppana and Raghavendra.

A new method to test system diagnosability

A new necessary and sufficient condition for t-diagnosability of a system is proposed. It is shown that the new scheme is computationally more efficient than the existing one for checking the diagnosability of a system.

Algebraic determination of circuits in a directed graph

An efficient method has been proposed in this paper to generate all directed circuits in a given arbitrary directed graph. A new concept, the reachability equation of a vertex, has been introduced to tackle the problem in a purely algebraic way.

On certain investigations on self-diagnosable systems

This paper presents a detailed investigation on various problems associated with the self-diagnosable digital systems. An efficient algorithm has been developed to check the t-diagnosability of a given system and several interesting results have been developed to optimize this checking procedure. The paper also embodies efficient solutions to the related problems of checking redundant edges, improving system diagnosability and identification of faulty units for a given output response.

A flexible architecture for multihop optical networks

It is desirable to have low diameter logical topologies for multihop lightwave networks. Researchers have investigated regular topologies for such networks. Only a few of these (e.g., GEMNET) are scalable to allow the addition of new nodes to an existing network. Adding new nodes to such networks requires a major change in routing scheme. For example, in a multistar implementation a large number of retuning of transmitters and receivers anti/or renumbering nodes are needed for GEMNET. We present a scalable logical topology which is not regular but it has a low diameter. This topology is interesting since it allows the network to be expanded indefinitely and new nodes can be added with a relatively small change to the network. We present the new topology, an algorithm to add nodes to the network and two routing schemes.

Checking p-t diagnosability of a system

In this paper the probabilistic measure of diagnosability, p-t diagnosability, originally proposed in [11], is used to study the diagnosability of digital systems. The system is represented by the graph theoretic model and assuming that failure probability of each unit is a priori known, a new necessary and sufficient condition has been proposed to check the p-t diagnosability of the system.

A new approach to single-fault-tolerant realization of synchronous sequential machines

Abstract This paper develops a new approach to the single-fault-tolerant realization of a given finite-state synchronous sequential machine by computing the correct state of the machine in a non-real-time mode. The computation is performed (by a checking clock pulse of higher frequency than the system clock of the machine) during the time interval between two successive state transitions of the machine. The proposed realization needs much less extra memory elements and associated combinational logic. And only a small portion of the required logic need be fault-tolerant.