Skip to main content
Top
Published in: The Journal of Supercomputing 3/2015

01-03-2015

The new Petersen-torus networks

Authors: Jong-Seok Kim, Hyeong-Ok Lee, Mihye Kim, Sung Won Kim

Published in: The Journal of Supercomputing | Issue 3/2015

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Routing and broadcasting are major parameters determining the performance of interconnection networks. In this paper, we propose a new Petersen-torus network \(\mathrm{NPT}(m, n)\) by modifying the external edge definitions of the Petersen-torus network to improve its diameter and broadcasting times. We also show one-to-all broadcasting algorithms in \(\mathrm{NPT}(m, n)\) using the single-link available and multiple-link available models.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Zhou W, Fan J, Jia X, Zhang S (2011) The spined cube: a new hypercube variant with smaller diameter. Inf Process Lett 111:561–567CrossRefMATHMathSciNet Zhou W, Fan J, Jia X, Zhang S (2011) The spined cube: a new hypercube variant with smaller diameter. Inf Process Lett 111:561–567CrossRefMATHMathSciNet
2.
go back to reference Johnsson SL (1987) Communication efficient basic linear algebra computations on hypercube architectures. J Parallel Distrib Comput 16:133–172CrossRef Johnsson SL (1987) Communication efficient basic linear algebra computations on hypercube architectures. J Parallel Distrib Comput 16:133–172CrossRef
3.
4.
go back to reference Albader B, Bose B, Flahive M (2012) Efficient communication algorithms in hexagonal mesh interconnection networks. IEEE Trans Parallel Distrib Syst 23(1):69–77CrossRef Albader B, Bose B, Flahive M (2012) Efficient communication algorithms in hexagonal mesh interconnection networks. IEEE Trans Parallel Distrib Syst 23(1):69–77CrossRef
5.
go back to reference Bai L, Maeda H, Ebara H, Nakano H (1998) A broadcasting algorithm with time and message optimum on arrangement graphs. J Graph Algorithms Appl 2(2):1–17CrossRefMathSciNet Bai L, Maeda H, Ebara H, Nakano H (1998) A broadcasting algorithm with time and message optimum on arrangement graphs. J Graph Algorithms Appl 2(2):1–17CrossRefMathSciNet
6.
go back to reference Carle J, Myoupo J-F, Seme D (1999) All-to-all broadcasting algorithms on honeycomb networks and applications. Parallel Process Lett 9(4):539–550CrossRef Carle J, Myoupo J-F, Seme D (1999) All-to-all broadcasting algorithms on honeycomb networks and applications. Parallel Process Lett 9(4):539–550CrossRef
7.
go back to reference Deazevedo MM, Bagherzadeh N, Latifi S (1995) Broadcasting algorithms for the star-connected cycles interconnection network. J Parallel Distrib Comput 25:209–222 Deazevedo MM, Bagherzadeh N, Latifi S (1995) Broadcasting algorithms for the star-connected cycles interconnection network. J Parallel Distrib Comput 25:209–222
8.
go back to reference Farah RN, Othman M (2014) Broadcasting communication in high degree modified chordal rings networks. Appl Math Inf Sci 8(1):229–233CrossRef Farah RN, Othman M (2014) Broadcasting communication in high degree modified chordal rings networks. Appl Math Inf Sci 8(1):229–233CrossRef
9.
go back to reference Mkwawa IM, Kouvatsos DD (2003) An optimal neighborhood broadcasting scheme for star interconnection networks. J Interconnect Netw 4(1):103–112CrossRef Mkwawa IM, Kouvatsos DD (2003) An optimal neighborhood broadcasting scheme for star interconnection networks. J Interconnect Netw 4(1):103–112CrossRef
10.
go back to reference Stewart IA (2014) Interconnection networks of degree three obtained by pruning two-dimensional tori. IEEE Trans Comput 63(10):2473–2486 Stewart IA (2014) Interconnection networks of degree three obtained by pruning two-dimensional tori. IEEE Trans Comput 63(10):2473–2486
11.
go back to reference Thomson A, Zhou S (2014) Frobenius circulant graphs of valency six, Eisenstein–Jacobi networks, and hexagonal meshes. Eur J Comb 38:61–78CrossRefMATHMathSciNet Thomson A, Zhou S (2014) Frobenius circulant graphs of valency six, Eisenstein–Jacobi networks, and hexagonal meshes. Eur J Comb 38:61–78CrossRefMATHMathSciNet
12.
go back to reference Yang X, Wang L, Yang L (2012) Optimal broadcasting for locally twisted cubes. Inf Process Lett 112:129–134CrossRefMATH Yang X, Wang L, Yang L (2012) Optimal broadcasting for locally twisted cubes. Inf Process Lett 112:129–134CrossRefMATH
13.
go back to reference Seo JH, Lee HO (2009) One-to-all broadcasting in Petersen-torus networks for SLA and MLA model. ETRI J 31(3):327–329CrossRef Seo JH, Lee HO (2009) One-to-all broadcasting in Petersen-torus networks for SLA and MLA model. ETRI J 31(3):327–329CrossRef
14.
15.
go back to reference Chen MS, Shin KG (1990) Addressing, routing, and broadcasting in hexagonal mesh multiprocessors. IEEE Trans Comput 39(1):10–18CrossRefMathSciNet Chen MS, Shin KG (1990) Addressing, routing, and broadcasting in hexagonal mesh multiprocessors. IEEE Trans Comput 39(1):10–18CrossRefMathSciNet
16.
go back to reference Tang KW, Padubidri SA (1994) Diagonal and toroidal mesh networks. IEEE Trans Comput 43(7):815–826CrossRefMATH Tang KW, Padubidri SA (1994) Diagonal and toroidal mesh networks. IEEE Trans Comput 43(7):815–826CrossRefMATH
17.
go back to reference Stojmenovic I (1997) Honeycomb network: topological properties and communication algorithms. IEEE Trans Parallel Distrib Syst 8(10):1036–1042CrossRef Stojmenovic I (1997) Honeycomb network: topological properties and communication algorithms. IEEE Trans Parallel Distrib Syst 8(10):1036–1042CrossRef
18.
go back to reference Arabnia HR, Oliver MA (1989) A transputer network for fast operations on digitised images. Int J Eurograph Assoc (Computer Graphics Forum) 8(1):3–12CrossRef Arabnia HR, Oliver MA (1989) A transputer network for fast operations on digitised images. Int J Eurograph Assoc (Computer Graphics Forum) 8(1):3–12CrossRef
19.
go back to reference Arabnia HR (1990) A parallel algorithm for the arbitrary rotation of digitized tmages using process-and-data-decomposition approach. J Parallel Distrib Comput 10(2):188–193CrossRef Arabnia HR (1990) A parallel algorithm for the arbitrary rotation of digitized tmages using process-and-data-decomposition approach. J Parallel Distrib Comput 10(2):188–193CrossRef
20.
go back to reference Bhandarkar SM, Arabnia HR (1995) The REFINE multiprocessor: theoretical properties and algorithms. Parallel Comput 21(11):1783–1806CrossRef Bhandarkar SM, Arabnia HR (1995) The REFINE multiprocessor: theoretical properties and algorithms. Parallel Comput 21(11):1783–1806CrossRef
21.
go back to reference Arabnia HR, Smith JW (1993) A reconfigurable interconnection network for imaging operations and its implementation using a multi-stage switching box. In: Proceedings of the 7th annual international high performance computing conference. The 1993 high performance computing: new horizons supercomputing symposium, pp 349–357 Arabnia HR, Smith JW (1993) A reconfigurable interconnection network for imaging operations and its implementation using a multi-stage switching box. In: Proceedings of the 7th annual international high performance computing conference. The 1993 high performance computing: new horizons supercomputing symposium, pp 349–357
22.
go back to reference Seo JH, Lee HO, Jang M (2008) Petersen-torus networks for multicomputer systems. In: Proceedings of the international conference on networked computing and advanced information management, pp 567–571 Seo JH, Lee HO, Jang M (2008) Petersen-torus networks for multicomputer systems. In: Proceedings of the international conference on networked computing and advanced information management, pp 567–571
23.
go back to reference Seo JH, Sim H, Park DH, Park JW, Lee YS (2011) One-to-one embedding between honeycomb mesh and Petersen-torus networks. Sensors 11:1959–1971CrossRef Seo JH, Sim H, Park DH, Park JW, Lee YS (2011) One-to-one embedding between honeycomb mesh and Petersen-torus networks. Sensors 11:1959–1971CrossRef
24.
go back to reference Seo JH, Jang M, Kim E, Ban K, Ryu N, Lee HO (2009) One-to-one embedding between hyper Petersen and Petersen-torus networks. Commun Comput Inf Sci 63:133–139CrossRef Seo JH, Jang M, Kim E, Ban K, Ryu N, Lee HO (2009) One-to-one embedding between hyper Petersen and Petersen-torus networks. Commun Comput Inf Sci 63:133–139CrossRef
25.
go back to reference Seo JH, Lee HO, Jang M, Kim E (2008) Node mapping algorithm between hypercube and Petersen-torus networks. In: Proceedings of the international conference on networked computing and advanced information management, pp 535–539 Seo JH, Lee HO, Jang M, Kim E (2008) Node mapping algorithm between hypercube and Petersen-torus networks. In: Proceedings of the international conference on networked computing and advanced information management, pp 535–539
26.
go back to reference Seo JH, Lee HO, Jang M, Han SH (2008) Node mapping algorithm between torus and Petersen-torus networks. In: Proceedings of the international conference on networked computing and advanced information management, pp 540–544 Seo JH, Lee HO, Jang M, Han SH (2008) Node mapping algorithm between torus and Petersen-torus networks. In: Proceedings of the international conference on networked computing and advanced information management, pp 540–544
27.
go back to reference Seo JH, Lee HO, Jang M (2008) Constructing complete binary trees on Petersen-torus networks. In: Proceedings of the international conference on computer sciences and convergence information technology, pp 252–255 Seo JH, Lee HO, Jang M (2008) Constructing complete binary trees on Petersen-torus networks. In: Proceedings of the international conference on computer sciences and convergence information technology, pp 252–255
28.
go back to reference Seo JH, Lee HO, Jang M (2008) Optimal routing and hamiltonian cycle in Petersen-torus networks. In: Proceedings of the international conference on computer sciences and convergence information technology, pp 303–308 Seo JH, Lee HO, Jang M (2008) Optimal routing and hamiltonian cycle in Petersen-torus networks. In: Proceedings of the international conference on computer sciences and convergence information technology, pp 303–308
29.
go back to reference Holton DA, Sheehan J (1993) The Petersen graph. Australian Mathematical Society lecture notes, vol 7. Cambridge University Press, London Holton DA, Sheehan J (1993) The Petersen graph. Australian Mathematical Society lecture notes, vol 7. Cambridge University Press, London
Metadata
Title
The new Petersen-torus networks
Authors
Jong-Seok Kim
Hyeong-Ok Lee
Mihye Kim
Sung Won Kim
Publication date
01-03-2015
Publisher
Springer US
Published in
The Journal of Supercomputing / Issue 3/2015
Print ISSN: 0920-8542
Electronic ISSN: 1573-0484
DOI
https://doi.org/10.1007/s11227-014-1342-3

Other articles of this Issue 3/2015

The Journal of Supercomputing 3/2015 Go to the issue

Premium Partner