NDLI: Fault tolerance of a class of connecting networks

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Fault tolerance of a class of connecting networks

Content Provider	ACM Digital Library
Author	Shen, John P. Hayes, John P.
Abstract	Several proposals have been made for using a class of connecting networks called β-networks in multicomputer systems, such as systems containing large numbers of microprocessors. A β-network is a network of 2 × 2 crossbar switches called β-elements. This paper presents an analysis of the fault tolerance of β-networks intended for multicomputer applications. A fault model is used which allows β-elements to be stuck in either of their two normal states. A new connectivity property called dynamic full access (DFA) is introduced which serves as the criterion for fault tolerance. A β-network is said to have the DFA property if each of its inputs can be connected to any of its outputs in a finite number of passes through the network. A fault is called critical if it destroys the DFA property. Two graph-theoretical characterizations of the critical faults of a β-network are presented. It is shown that there is a one-to-one correspondence between minimal critical faults and the cutsets of the circuit adjacency graphs derived from the β-network. It is further shown that a fault is critical if and only if it is incompatible with all Eulerian circuits associated with the β-network. Some applications of the theory are discussed.
Starting Page	61
Ending Page	71
Page Count	11
File Format	PDF
DOI	10.1145/800053.801910
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1980-05-06
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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