Abstract.
The class of dense circulant graphs of degree four with optimal distance-related properties is analyzed in this paper. An algebraic study of this class is done. Two geometric characterizations are given, one in the plane and other in the space. Both characterizations facilitate the analysis of their topological properties and corroborate their suitability for implementing interconnection networks for distributed and parallel computers. Also a distance-hereditary non-disjoint decomposition of these graphs into rings is computed. Besides its practical consequences, this decomposition allows us the presentation of these optimal circulant graphs as a particular evolution of the traditional ring topology.
This work has been partially supported by the Spanish CICYT project TIC2001-0591-C02-01 and by the Spanish Ministry of Education under grants FP-2001-2482,PR2002-0043 and BFM2001-1294.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Adám, A.: Research problem 2-10. J. Combinatorial Theory 393, 1109–1124 (1991)
Adiga, N., et al.: An Overview of the BlueGene/L Supercomputer. In: Supercomputing 2002 (November 2002)
Arden, B.W., Lee, H.: Analysis of Chordal Ring Networks. IEEE Transactions on Computers C-30(4), 291–295 (1981)
Beivide, R., Herrada, E., Balczar, J.L., Arruabarrena, A.: Optimal Distance Networks of Low Degree for Parallel Computers. IEEE Transactions on Computers C-40(10), 1109–1124 (1991)
Bermond, J.-C., Comellas, F., Hsu, D.F.: Distributed Loop Computer Networks: A Survey. Journal of Parallel and Distributed Computing 24, 2–10 (1995)
Bose, B., Broeg, B., Known, Y., Ashir, Y.: Lee Distance and Topological Properties of k-ary n-cubes. IEEE Transactions on
Computers, W.J.: The Illiac IV System. Proc. IEEE 44(8), 1021–1030 (1995); Bouknight, W.J., Denenberg, S.A., McIntyre, D.E., Randall, J.M., Sameh, A.H., Slotnick, D.L.: The Illiac IV System. Proc. IEEE 60(4), 369–388 (1972)
Fiol, M.A., Yebra, J.L., Alegre, I., Valero, M.: A Discrete Optimization Problem in Local Networks and Data Alignment. IEEE Transactions on Computers 36(6), 702–713 (1987)
Huber, K.: Codes over Tori. IEEE Trans. on Information Theory 43(2), 740–744 (1997)
LaForge, L.E., Korver, K.F., Fadali, M.S.: What Designers of Bus and Network Architectures Should Know about Hypercubes. IEEE Transactions on Computers 52(4), 525–544 (2003)
Lau, C.M., Chen, G.: Optimal Layouts of Midimew Networks. IEEE Transactions on Parallel and Distributed Systems 7(9), 954–961 (1996)
Martínez, C., Beivide, R., Izu, C., Gutierrez, J.: Distance-Hereditary Embeddings of Circulant Graphs. In: Proc. of IEEE Int. Conf. on Information Technology: Coding and Computing (ITCC-2003), Las Vegas, pp. 320-324 (2003)
Mukherjee, S., Bannon, P., Lang, S., Spink, A., Webb, D.: The Alpha 21364 Network Architecture. IEEE Micro 22(1), 26–35 (2002)
Puente, V., Izu, C., Gregorio, J.A., Beivide, R., Prellezo, J.M., Vallejo, F.: Rearranging Links to Improve the Performance of Parallel Computers: The Case of Midimew Networks. In: Proc. of International Conference on Supercomputing. ICS 2000. pp. 44-53 (2000)
Wilkov, R.S.: Analysis and Design of Reliable Computer Networks. IEEE Trans. On Communications 20, 660–678 (1972)
Wong, C.K., Coppersmith, D.: A Combinatorial Problem Related to Multimodule Memory Organizations. Journal of the ACM 21(3), 392–402 (1974)
Yang, Y., Funashashi, A., Jouraku, A., Nishi, H., Amano, H., Sueyoshi, T.: Recursive Diagonal Torus: An Interconnection Network for Massively Parallel Computers. IEEE Transactions on Parallel and Distributed Systems 12(7), 701–715 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Beivide, R., Martínez, C., Izu, C., Gutierrez, J., Gregorio, JÁ., Miguel-Alonso, J. (2003). Chordal Topologies for Interconnection Networks. In: Veidenbaum, A., Joe, K., Amano, H., Aiso, H. (eds) High Performance Computing. ISHPC 2003. Lecture Notes in Computer Science, vol 2858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39707-6_33
Download citation
DOI: https://doi.org/10.1007/978-3-540-39707-6_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20359-9
Online ISBN: 978-3-540-39707-6
eBook Packages: Springer Book Archive