A measure of the performance of binomial interconnection networks

• Published in: Computers & electrical engineering Vol. 18; no. 5; pp. 411 - 420
• Main Author: Khanna, Sanjay
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Ltd 1992; Pergamon
• Subjects: Applied sciences; Circuit properties; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Switching, multiplexing, switched capacity circuits; Multiprocessor; Computer peripheral; Capacity; Interconnection; Telecommunication switching; Computer system; Distributed system; Switching circuit; Switching; Optimization
• ISSN: 0045-7906; 1879-0755
• DOI: 10.1016/0045-7906(92)90047-H

An important measure of the performance of an interconnection network is its capacity. The capacity of an ( m d ) binomial network is discussed as a measure of the average number of inputs that can be connected to the outputs. It is shown that for input subset of size less than or equal to d + 2, all inputs can be connected to outputs. For input subset of size greater than d + 2, the network is considered in terms of its prime decomposition class (pdc). We present an empirical formula for the capacity of ( m d ) networks based on the number of configurations and capacity contribution of different factors in the pdc. It is shown that an ( m d ) binomial network can provide capacity close to that of the complete crossbar switch while avoiding the latter's expensive hardware cost of contact switches. Next, we suggest a method to maximize the capacity of binomial network when selecting inputs. We illustrate how concepts of constant weight codes and residue classes can be applied to construct a type of ( m d ) network called Optimally Designed Binomial (ODB) Network. We present an algorithm which selects inputs corresponding to different residue classes and uses the left cyclic shift feature to optimize the capacity of the network.