Conditional Fault-Diameter of Torus Networks

• Main Authors: Abderezak Touzene, Khaled Day
• Format: Article
• Language: English
• Published: Sultan Qaboos University 2005-06-01
• Series: Sultan Qaboos University Journal for Science
• Subjects: Fault-tolerance, forbidden faulty sets, torus, node connectivity, conditional node connectivity, conditional fault-diameter, fault-tolerant routing.
• Online Access: https://journals.squ.edu.om/index.php/squjs/article/view/331

We obtain the conditional fault-diameter of the square torus interconnection network under the condition of forbidden faulty sets (i.e. assuming that each non-faulty processor has at least one non-faulty neighbor). We show that under this condition, the square torus, whose connectivity is 4, can tolerate up to 5 faulty nodes without becoming disconnected. The conditional node connectivity is, therefore, 6. We also show that the conditional fault-diameter of the square torus is equal to the fault-free diameter plus two. With this result the torus joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault-diameter has been shown to be only two units over the fault-free diameter. Two fault-tolerant routing algorithms are discussed based on the proposed vertex disjoint paths construction.