Journal ArticleDOI
Honeycomb networks: Topological properties and communication algorithms
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The honeycomb mesh, based on hexagonal plane tessellation, is considered as a multiprocessor interconnection network and honeycomb networks with rhombus and rectangle as the bounding polygons are considered.Abstract:
The honeycomb mesh, based on hexagonal plane tessellation, is considered as a multiprocessor interconnection network. A honeycomb mesh network with n nodes has degree 3 and diameter /spl ap/1.63/spl radic/n-1, which is 25 percent smaller degree and 18.5 percent smaller diameter than the mesh-connected computer with approximately the same number of nodes. Vertex and edge symmetric honeycomb torus network is obtained by adding wraparound edges to the honeycomb mesh. The network cost, defined as the product of degree and diameter, is better for honeycomb networks than for the two other families based on square (mesh-connected computers and tori) and triangular (hexagonal meshes and tori) tessellations. A convenient addressing scheme for nodes is introduced which provides simple computation of shortest paths and the diameter. Simple and optimal (in the number of required communication steps) routing, broadcasting, and semigroup computation algorithms are developed. The average distance in honeycomb torus with n nodes is proved to be approximately 0.54/spl radic/n. In addition to honeycomb meshes bounded by a regular hexagon, we consider also honeycomb networks with rhombus and rectangle as the bounding polygons.read more
Citations
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Journal ArticleDOI
Leap Zagreb Connection Numbers for Some Networks Models
TL;DR: In this paper, the exact values of the topological indices which play a vital role in studying chemical information, structure properties like QSAR and QSPR have been determined, and analogous graph invariants, based on the second degrees of vertices, called leap Zagreb indices have been considered.
Journal ArticleDOI
On Planar Tessellations and Interference Estimation in Wireless Ad-Hoc Networks
TL;DR: A geometric probabilistic model is considered for interference estimation in wireless ad-hoc networks, utilizing the distance distributions for hexagonal and square tessellations.
Journal ArticleDOI
A Group Construction Method with Applications to Deriving Pruned Interconnection Networks
Wenjun Xiao,Behrooz Parhami +1 more
TL;DR: It is shown that, under certain conditions, Cayley graphs based on the constructed groups are pruned networks when Cayley graph of the original commutative groups are kD tori.
Journal ArticleDOI
The L (2,1)-labelling problem for cubic Cayley graphs on dihedral groups
TL;DR: It is proved that the λ-number of such a graph is between 5 and 7, and moreover the characterisation of such graphs with κ-number 5 is given.
References
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Book
Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes
TL;DR: This chapter discusses sorting on a Linear Array with a Systolic and Semisystolic Model of Computation, which automates the very labor-intensive and therefore time-heavy and expensive process of manually sorting arrays.
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Book Review: Introduction to Parallel Algorithms and Architectures : Arrays, Trees, Hypercubes by F. T. Leighton (Morgan Kauffman Pub, 1992)
TL;DR: The author, a well-known researcher in paralle l computing, once again has proved his expertise and authority on the materials covered and this book will certainly have an impact to the psychology of students and researchers alike.
Book
Parallel computation: models and methods
TL;DR: This chapter discusses models of Computation, Combinational Circuits, and Parallel Synergy, which aims to explain the construction of parallel circuits and their applications in medicine and engineering.
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Addressing, routing, and broadcasting in hexagonal mesh multiprocessors
TL;DR: 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, independent of the network's size.
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Parallel Computation: Models And Methods
TL;DR: This book is an excellent practical guide in modern parallel scientific programming, and it can be used for self-instruction and also for all specialists who are interested in parallel scientific computing.