On Permutations Passable by the Gamma Network

Abstract The Gamma network is a multiprocessor interconnection network with redundant paths between source and destination terminals. The basic switching element in this network is a 3 × 3 crossbar, and the stages are linked by “power of two” and identity connections. The Gamma network is known to realize many classes of permutations useful in parallel processing, and in this paper a detailed study of various classes of permutations passable by the network with a simple control algorithm is presented. Conditions for passability of an arbitrary permutation with this algorithm have been formulated and used to show that several useful classes of permutations in parallel processing can be realized. Although the algorithm does not utilize the full connection capability of the network, it produces conflict-free routing for most of the useful classes of permutations the network is capable of passing.

[1]  V. Benes,et al.  Mathematical Theory of Connecting Networks and Telephone Traffic. , 1966 .

[2]  Douglas Stott Parker,et al.  Notes on Shuffle/Exchange-Type Switching Networks , 1980, IEEE Transactions on Computers.

[3]  Robert J. McMillen,et al.  Routing Schemes for the Augmented Data Manipulator Network in an MIMD System , 1982, IEEE Transactions on Computers.

[4]  Marshall C. Pease,et al.  The Indirect Binary n-Cube Microprocessor Array , 1977, IEEE Transactions on Computers.

[5]  Harold S. Stone,et al.  Parallel Processing with the Perfect Shuffle , 1971, IEEE Transactions on Computers.

[6]  Jacques Lenfant,et al.  Parallel Permutations of Data: A Benes Network Control Algorithm for Frequently Used Permutations , 1978, IEEE Transactions on Computers.

[7]  Pen-Chung Yew,et al.  An Easily Controlled Network for Frequently Used Permutations , 1981, IEEE Transactions on Computers.

[8]  Duncan H. Lawrie,et al.  Access and Alignment of Data in an Array Processor , 1975, IEEE Transactions on Computers.

[9]  Howard Jay Siegel,et al.  Many SIMD interconnection networks have been proposed . To put the different approaches into perspective , this analysis compares a number of single-and multistage networks , 2022 .

[10]  D. C. Opferman,et al.  On a class of rearrangeable switching networks part I: Control algorithm , 1971 .

[11]  Sartaj Sahni,et al.  Parallel Algorithms to Set Up the Benes Permutation Network , 1982, IEEE Transactions on Computers.

[12]  Tse-Yun Feng,et al.  Data Manipulating Functions in Parallel Processors and Their Implementations , 1974, IEEE Transactions on Computers.

[13]  Cauligi S. Raghavendra,et al.  The Gamma Network , 1984, IEEE Transactions on Computers.

[14]  Robert J. McMillen,et al.  Using the Augmented Data Manipulator Network in PASM , 1981, Computer.