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The new Petersen-torus networks

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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.

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References

  1. Zhou W, Fan J, Jia X, Zhang S (2011) The spined cube: a new hypercube variant with smaller diameter. Inf Process Lett 111:561–567

    Article  MATH  MathSciNet  Google Scholar 

  2. Johnsson SL (1987) Communication efficient basic linear algebra computations on hypercube architectures. J Parallel Distrib Comput 16:133–172

    Article  Google Scholar 

  3. Mendia VE, Sarkar D (1992) Optimal broadcasting on the star graph. IEEE Trans Parallel Distrib Syst 3(4):389–396

    Article  MathSciNet  Google Scholar 

  4. Albader B, Bose B, Flahive M (2012) Efficient communication algorithms in hexagonal mesh interconnection networks. IEEE Trans Parallel Distrib Syst 23(1):69–77

    Article  Google Scholar 

  5. 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):1–17

    Article  MathSciNet  Google Scholar 

  6. Carle J, Myoupo J-F, Seme D (1999) All-to-all broadcasting algorithms on honeycomb networks and applications. Parallel Process Lett 9(4):539–550

    Article  Google Scholar 

  7. Deazevedo MM, Bagherzadeh N, Latifi S (1995) Broadcasting algorithms for the star-connected cycles interconnection network. J Parallel Distrib Comput 25:209–222

  8. Farah RN, Othman M (2014) Broadcasting communication in high degree modified chordal rings networks. Appl Math Inf Sci 8(1):229–233

    Article  Google Scholar 

  9. Mkwawa IM, Kouvatsos DD (2003) An optimal neighborhood broadcasting scheme for star interconnection networks. J Interconnect Netw 4(1):103–112

    Article  Google Scholar 

  10. Stewart IA (2014) Interconnection networks of degree three obtained by pruning two-dimensional tori. IEEE Trans Comput 63(10):2473–2486

  11. Thomson A, Zhou S (2014) Frobenius circulant graphs of valency six, Eisenstein–Jacobi networks, and hexagonal meshes. Eur J Comb 38:61–78

    Article  MATH  MathSciNet  Google Scholar 

  12. Yang X, Wang L, Yang L (2012) Optimal broadcasting for locally twisted cubes. Inf Process Lett 112:129–134

    Article  MATH  Google Scholar 

  13. Seo JH, Lee HO (2009) One-to-all broadcasting in Petersen-torus networks for SLA and MLA model. ETRI J 31(3):327–329

    Article  Google Scholar 

  14. Dally W, Seitz C (1986) The torus routing chip. Distrib Comput 1:187–196

    Article  Google Scholar 

  15. Chen MS, Shin KG (1990) Addressing, routing, and broadcasting in hexagonal mesh multiprocessors. IEEE Trans Comput 39(1):10–18

    Article  MathSciNet  Google Scholar 

  16. Tang KW, Padubidri SA (1994) Diagonal and toroidal mesh networks. IEEE Trans Comput 43(7):815–826

    Article  MATH  Google Scholar 

  17. Stojmenovic I (1997) Honeycomb network: topological properties and communication algorithms. IEEE Trans Parallel Distrib Syst 8(10):1036–1042

    Article  Google Scholar 

  18. Arabnia HR, Oliver MA (1989) A transputer network for fast operations on digitised images. Int J Eurograph Assoc (Computer Graphics Forum) 8(1):3–12

    Article  Google Scholar 

  19. 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):188–193

    Article  Google Scholar 

  20. Bhandarkar SM, Arabnia HR (1995) The REFINE multiprocessor: theoretical properties and algorithms. Parallel Comput 21(11):1783–1806

    Article  Google Scholar 

  21. 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. 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. Seo JH, Sim H, Park DH, Park JW, Lee YS (2011) One-to-one embedding between honeycomb mesh and Petersen-torus networks. Sensors 11:1959–1971

    Article  Google Scholar 

  24. 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 63:133–139

    Article  Google Scholar 

  25. 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. 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. 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. 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. Holton DA, Sheehan J (1993) The Petersen graph. Australian Mathematical Society lecture notes, vol 7. Cambridge University Press, London

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Acknowledgments

We thank the reviewers for their comments and suggestions which have substantially improved our presentation. This work was supported by the 2012 Yeungnam University Research Grant. Also, this research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology(2012R1A1A4A01014439).

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Authors and Affiliations

  1. Department of Mathematics and Physics, North Carolina Central University, Durham, NC, 27707, USA

    Jong-Seok Kim

  2. Department of Computer Education, Sunchon National University, Sunchon, Chonnam, 540-742, South Korea

    Hyeong-Ok Lee

  3. Department of Computer Science Education, Catholic University of Daegu, Gyeongsan, Gyeongbuk, 712-702, South Korea

    Mihye Kim

  4. Department of Information and Communication Engineering, Yeungnam University, Gyeongsan, Gyeongbuk, 712-749, South Korea

    Sung Won Kim

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  1. Jong-Seok Kim
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  2. Hyeong-Ok Lee
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Correspondence to Sung Won Kim.

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Kim, JS., Lee, HO., Kim, M. et al. The new Petersen-torus networks. J Supercomput 71, 894–908 (2015). https://doi.org/10.1007/s11227-014-1342-3

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  • DOI: https://doi.org/10.1007/s11227-014-1342-3

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