Optimally Embedding 3-Ary n-Cubes into Grids

The 3-ary n -cube, denoted as Q n 3 , is an important interconnection network topology proposed for parallel computers, owing to its many desirable properties such as regular and symmetrical structure, and strong scalability, among others. In this paper, we first obtain an exact formula for the mini...

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Bibliographic Details
Published inJournal of computer science and technology Vol. 34; no. 2; pp. 372 - 387
Main Authors Fan, Wei-Bei, Fan, Jian-Xi, Lin, Cheng-Kuan, Wang, Yan, Han, Yue-Juan, Wang, Ru-Chuan
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2019
Springer Nature B.V
School of Computer Science and Technology, Soochow University, Suzhou 215006, China
Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing 210003, China%College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China%School of Computer Science and Technology, Soochow University, Suzhou 215006, China%Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing 210003, China
Subjects
Algorithms
Arrays
Artificial Intelligence
Communication
Computer centers
Computer Science
Computers
Cubes
Data Structures and Information Theory
Embedding
Graphs
Information Systems Applications (incl.Internet)
Network topologies
Parallel computers
R&D
Regular Paper
Research & development
Software Engineering
Symmetry
Theory of Computation
embedding algorithm
3-ary
cube
interconnection network
grid
3-ary n-cube
Online AccessGet full text
ISSN1000-9000
1860-4749
DOI10.1007/s11390-019-1893-0

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Summary:The 3-ary n -cube, denoted as Q n 3 , is an important interconnection network topology proposed for parallel computers, owing to its many desirable properties such as regular and symmetrical structure, and strong scalability, among others. In this paper, we first obtain an exact formula for the minimum wirelength to embed Q n 3 into grids. We then propose a load balancing algorithm for embedding Q n 3 into a square grid with minimum dilation and congestion. Finally, we derive an O ( N 2 ) algorithm for embedding Q n 3 into a gird with balanced communication, where N is the number of nodes in Q n 3 . Simulation experiments are performed to verify the total wirelength and evaluate the network cost of our proposed embedding algorithm.
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ISSN:1000-9000
1860-4749
DOI:10.1007/s11390-019-1893-0