Addressing, Routing, and Broadcasting in Hexagonal Mesh Multiprocessors

A family of six-regular graphs, called hexagonal meshes or H-meshes, is considered as a multiprocessor interconnection network. Processing nodes on the periphery of an H-mesh are first wrapped around to achieve regularity and homogeneity. The diameter of a wrapped H-mesh is shown to be of O(p/sup 1/2/), where p is the number of nodes in the H-mesh. An elegant, distributed routing scheme is developed for wrapped H-meshes so that each node in an H-mesh can compute shortest paths from itself to any other node with a straightforward algorithm of O(1) using the addresses of the source-destination pair only, i.e. independent of the network's size. This is in sharp contrast with those previously known algorithms that rely on using routing tables. Furthermore, the authors also develop an efficient point-to-point broadcasting algorithm for the H-meshes which is proved to be optimal in the number of required communication steps. The wrapped H-meshes are compared against some other existing multiprocessor interconnection networks, such as hypercubes, trees, and square meshes. The comparison reinforces the attractiveness of the H-mesh architecture. >

[1]  James Turner.  Point-symmetric graphs with a prime number of points , 1967 .

[2]  Frank Harary,et al.  Graph Theory , 2016 .

[3]  R. Halin.  A theorem on n-connected graphs , 1969 .

[4]  S. Hakimi.  An Algorithm for Construction of the Least Vulnerable Communication Network or the Graph with the Maximum Connectivity , 1969 .

[5]  M. Watkins.  Connectivity of transitive graphs , 1970 .

[6]  F. Boesch,et al.  On graphs of invulnerable communication nets , 1970 .

[7]  R. Wilkov,et al.  Analysis and Design of Reliable Computer Networks , 1972, IEEE Trans. Commun..

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

[9]  William A. Wulf,et al.  HYDRA , 1974, Commun. ACM.

[10]  E. Douglas Jensen,et al.  Computer Interconnection Structures: Taxonomy, Characteristics, and Examples , 1975, CSUR.

[11]  David L. Mills,et al.  An overview of the distributed computer network , 1899, AFIPS '76.

[12]  Marvin H. Solomon,et al.  Processor Interconnection Strategies , 1980, IEEE Transactions on Computers.

[13]  Tse-Yun Feng,et al.  On a Class of Multistage Interconnection Networks , 1980, IEEE Transactions on Computers.

[14]  Tse-yun Feng,et al.  A Survey of Interconnection Networks , 1981, Computer.

[15]  B W Arden,et al.  Analysis of Chordal Ring Network , 1981, IEEE Transactions on Computers.

[16]  Larry D. Wittie,et al.  Communication Structures for Large Networks of Microcomputers , 1981, IEEE Transactions on Computers.

[17]  Carlo H. Séquin,et al.  Hypertree: A Multiprocessor Interconnection Topology , 1981, IEEE Transactions on Computers.

[18]  Ellis Horowitz,et al.  The Binary Tree as an Interconnection Network: Applications to Multiprocessor Systems and VLSI , 1981, IEEE Transactions on Computers.

[19]  Alain J. Martin.  The Torus: An Exercise in Constructing a Processing Surface , 1982 .

[20]  Charles L. Seitz,et al.  The cosmic cube , 1985, CACM.

[21]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[22]  Kenneth S. Stevens,et al.  The Post Office-Communication Support for Distributed Ensemble Architectures , 1986, IEEE International Conference on Distributed Computing Systems.

[23]  S. Lennart Johnsson,et al.  Distributed Routing Algorithms for Broadcasting and Personalized Communication in Hypercubes , 1986, ICPP.

[24]  Kai Hwang,et al.  Hypernet: A Communication-Efficient Architecture for Constructing Massively Parallel Computers , 1987, IEEE Transactions on Computers.