Abstract
The problem of all-to-all communication in a network consists of designing directed paths between any ordered pair of vertices in a symmetric directed graph and assigning them minimum number of colours such that every two dipaths sharing an edge have distinct colour. We prove several exact results on the number of colours for some Cartesian product graphs, including 2-dimensional (toroidal) square meshes of odd side, which completes previous results for even sided square meshes.
This research was supported by grant No. 95/5305/277 of Slovak Grant Agency and by grant of British Council to the Project Loughborough Reconfigurable Array and Theoretical Aspects of Interconnection Networks. The research of the last two authors was supported also by the grant of EU INCO-COP 96-0195.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Amar, D., Raspaud, A., Togni, O., Total exchange in the optical networks created by composition of cliques. Manuscript, September 1996.
Beauquier, B., All-to-all communication for some wavelength-routed all-optical networks, submitted to Networks.
Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U., Graph problems arising from wavelength routing in all optical networks, to appear in: Proc. of WOCS'97, 1997.
Beauquier, B., Paulraja, P. personal communication, 1997.
Bermond, J.-C., personal communication, 1997.
Bermond, J.-C., Gargano, L., Perennes, S., Rescigno, A., Vaccaro, U., Efficient collective communications in optical networks, in: Proc. of 23rd Intl. Colloquium on Automata Languaages and Programming, Lecture Notes in Computer Science 1099, Springer Verlag, Berlin, 1996.
Gargano, L., Hell, P., Perennes, S., Coloring all directed paths in symmetric tree, Manuscript, 1996.
Leighton, F. T., Introduction to Parallel Algorithms and Architectures. Morgan Kaufmann Publishers, Inc.,1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schröder, H., Sýkora, O., Vrt'o, I. (1997). Optical all-to-all communication for some product graphs (Extended Abstract). In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_138
Download citation
DOI: https://doi.org/10.1007/3-540-63774-5_138
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63774-5
Online ISBN: 978-3-540-69645-2
eBook Packages: Springer Book Archive