Summary
In this paper, on analysis of the properties of modified chordal ring 4\(^\textrm{th}\) degree topologies has been presented. Two special types of these structures, namely optimal and ideal graphs, have been defined. The basic parameters (diameter and average path distance) were calculated and described by approximate formulas which makes possible to evaluate these parameters for any modified graph proposed by authors, and it gives possibility to model the properties of these networks without requiring any specific path calculation between pairs of nodes which may be time and resource consuming for large scale systems. In the last part of paper the comparison of the analyzing structures and reference graph has been carry out.
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
Bhuyan, L.N.: Interconnection Networks for Parallel and Distributed Processing. IEEE Computer 20(6), 9–12 (1987)
Kotsis, G.: Interconnection Topologies and Routing for Parallel Processing Systems. ACPC, Technical Report Series, ACPC/TR92-19 (1992)
Bujnowski, S., Dubalski, B., Pedersen, J.M., Zabłudowski, A.J.: Analysis of Regular Structures Third Degree Based on Chordal Rings. Image Processing & Communications 14(1), 13–24 (2009)
Bujnowski, S., Dubalski, B.z., Zabłudowski, A., Ledźinski, D., Marciniak, T., Pedersen, J.M.: Comparison of Modified Degree 6 Chordal Rings. In: Choraś, R.S. (ed.) Image Processing and Communications Challenges 2. AISC, vol. 84, pp. 435–445. Springer, Heidelberg (2010)
Bujnowski, S., Dubalski, B.z., Zabłudowski, A., Pedersen, J.M., Riaz, T.: Analysis of Degree 5 Chordal Rings for Network Topologies. In: Choraś, R.S. (ed.) Image Processing and Communications Challenges 3. AISC, vol. 102, pp. 445–457. Springer, Heidelberg (2011)
Dubalski, B., Bujnowski, S., Ledziński, D., Zabłudowski, A., Kiedrowski, P.: Analysis of Modified Fifth Degree Chordal Rings. In: New Frontiers in Graph Theory, pp. 43–88. InTech (2012) ISBN 978-953-51-0115-4
Zabłudowski, Ł., Dubalski, B., Kiedrowski, P., Ledziński, D., Marciniak, T.: Modified NDR structures. Image Processing & Communications 17(3), 29–47 (2012) ISSN 1425-140X
Narayanan, L., Opatrny, J.: Compact Routing on Chordal Rings of Degree Four. Algorithmica 23, 72–96 (1999)
Comellas, F., Mitjana, M., Narayanan, L., Opatrny, J.: Optical routing of uniform instances in tori. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 285–294. Springer, Heidelberg (2000)
Narayanan, L., Opatrny, J., Sotteau, D.: All-To-All Optical Routing in Chordal Rings of Degree 4. Algorithmica 31, 155–178 (2001)
Bermond, J.C., Comellas, F., Hsu, D.: Distributed Loop Computer Networks: A Survey. Journal of Parallel and Distributed Computing 24, 2–10 (1995)
Diestel, R.: Graph Theory, 4th edn. Graduate Texts in Mathematics, vol. 173. Springer, Heidelberg (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ledziński, D., Bujnowski, S., Marciniak, T., Pedersen, J.M., Lopez, J.G. (2014). Network Structures Constructed on Basis of Chordal Rings 4th Degree. In: S. Choras, R. (eds) Image Processing and Communications Challenges 5. Advances in Intelligent Systems and Computing, vol 233. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-01622-1_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-01622-1_33
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-01621-4
Online ISBN: 978-3-319-01622-1
eBook Packages: EngineeringEngineering (R0)