Abstract
Recently, the WK-recursive network has received much attention due to its many favorable properties such as a high degree of scalability. By K(d,t), we denote the WK-recursive network of level t, each of whose basic modules is a d-node complete graph, where d > 1 and t ≥ 1. In this paper, we construct fault-free Hamiltonian cycles in K(d, t) with at most d – 3 faulty nodes, where d ≥ 4. Since the connectivity of K(d, t) is d – 1, the result is optimal.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Della Vecchia, G., Sanges, C.: Recursively scalable networks for message passing architectures. In: Chiricozzi, E., D’Amico, A. (eds.) Parallel Processing and Applications, pp. 33–40. Elsevier North-Holland, Amsterdam (1988)
INMOS Limited: Transputer reference manual. Prentice-Hall, Upper Saddle River, NJ 07458, USA, Includes index. Bibliography: pp. 315-324 (1988)
Della Vecchia, G., Sanges, C.: A recursively scalable network VLSI implementation. Future Generation Computer Systems 4, 235–243 (1988)
Della Vecchia, G., Sanges, C.: An optimized broadcasting technique for WK-recursive topologies. Future Generation Computer Systems 5, 353–357 (1989/1990)
Chen, G.H., Duh, D.R.: Topological properties, communication, and computation on WK-recursive networks. Networks 24, 303–317 (1994)
Duh, D.R., Chen, G.H.: Topological properties of WK-recursive networks. Journal of Parallel and Distributed Computing 23, 468–474 (1994)
Fernandes, R., Friesen, D.K., Kanevsky, A.: Embedding rings in recursive networks. In: Proceedings of the 6th Symposium on Parallel and Distributed Processing, pp. 273–280 (1994)
Fernandes, R., Friesen, D.K., Kanevsky, A.: Efficient routing and broadcasting in recursive interconnection networks. In: Proceedings of the 23rd International Conference on Parallel Processing. Architecture, vol. 1, pp. 51–58 (1994)
Fernandes, R., Kanevsky, A.: Substructure allocation in recursive interconnection networks. In: Proceedings of the 1993 International Conference on Parallel Processing. Architecture, vol. 1, pp. 319–323 (1993)
Verdoscia, L., Vaccaro, R.: An adaptive routing algorithm for WK-recursive topologies. Computing 63, 171–184 (1999)
Verdoscia, L., Scafuri, U.: CODACS project: level-node communication policies. In: Proceedings of the Eleventh Euromicro Conference on Parallel, Distributed and Network-Based Processing, pp. 134–139 (2003)
Della Vecchia, G., Distasi, R.: B-Tree triangular coding on WK-recursive networks. In: Parallel Computing: State-of-the-Art and Perspectives, Proceedings of the Conference ParCo 1995, Ghent, Belgium, September 19-22, Advances in Parallel Computing, vol. 11, pp. 165–172, Amsterdam, Elsevier, North-Holland (1996)
Liaw, S.C., Chang, G.J.: Generalized diameters and rabin numbers of networks. Journal of Combinatorial Optimization 2, 371–384 (1999)
Fu, J.S.: Hamiltonian-connectedness of the WK-recursive network. In: Proceedings of the 7th International Symposium on Parallel Architectures, Algorithms and Networks, pp. 569–574 (2004)
Akl, S.G.: Parallel Computation: Models and Methods. Prentice-Hall, Upper Saddle River (1997)
Leighton, F.T.: Introduction to Parallel Algorithms and Architectures: arrays. trees. hypercubes. Morgan Kaufman, San Mateo (1992)
Ascheuer, N.: Hamiltonian path problems in the on-line optimization of flexible manufacturing systems. PhD thesis, University of Technology, Berlin, Germany (1995), Also available at ftp://ftp.zib.de/pub/zib-publications/reports/TR-96-03.ps
Buckley, F., Harary, F.: Distance in Graphs. Addison-Wesley, Reading (1990)
Harary, F., Hayes, J.P.: Edge fault tolerance in graphs. Networks 23, 135–142 (1993)
Fu, J.S., Chen, G.H.: Fault-tolerant cycle embedding in hierarchical cubic networks. Networks 43, 28–38 (2004)
Huang, W.T., Tan, J.M., Hung, C.N., Hsu, L.H.: Fault-tolerant hamiltonicity of twisted cubes. Journal of Parallel and Distributed Computing 62, 591–604 (2002)
Fu, J.S.: Fault-tolerant cycle embedding in the hypercube. Parallel Computing 29, 821–832 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fu, JS. (2004). Fault-Tolerant Cycle Embedding in the WK-Recursive Network. In: Cao, J., Yang, L.T., Guo, M., Lau, F. (eds) Parallel and Distributed Processing and Applications. ISPA 2004. Lecture Notes in Computer Science, vol 3358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30566-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-30566-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24128-7
Online ISBN: 978-3-540-30566-8
eBook Packages: Computer ScienceComputer Science (R0)