Abstract
Linear Interval Routing is a space-efficient routing method for point-to-point communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wrap-around. A common way to measure the efficiency of such routing methods is in terms of the maximal length of a path a message traverses. For Interval Routing the upper bound and lower bound on this quantity are 2D and 1.75D — 1, respectively, where D is the diameter of the network. We prove a lower bound of Ω(D2) on the length of a path a message traverses under Linear Interval Routing. We further extend the result by showing a connection between the efficiency of Linear Interval Routing and the bi-diameter of the network.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Bakker, E.M., van Leeuwen, J., Tan, R.B.: Prefix Routing Schemas in Dynamic Networks. Tech. Rep. RUU-CS-90-10, Dept. of Computer science, Utrecht University, Utrecht (1990).
Bakker, E.M., van Leeuwen, J., Tan, R.B.: Linear Interval Routing. Algorithms Review 2 (1991) 45–61.
Dinitz, Y., Private communication.
Even, S.: Graph Algorithms. Computer Science Press, Inc., (1979).
Eilam, T., Moran, S., Zaks, S.: Bi-Diameter in 2-Edge-Connected Graphs. In preparation.
Fraigniaud, P., Gavoile, C.: Interval Routing Schemes. Research Rep. 94-04, LIPS-ENS Lyon (1994).
Li, Q., Sotteau, D., Xu, J.: 2-Diameter of De Bruijn Networks. Rapport de Recherche 950, Universite de Paris Sud, centre d'Orsay, Laboratoire de Recherche en Informatique, 91405 Orsay, France (1995).
van Leeuwen, J., Tan, R.B.: Routing with Compact Routing Tables. Tech. Rep. RUU-CS-83-16, Dept. of Computer Science, Utrecht University (1983). Also as: Computer Networks with Compact Routing Tables. In: G. Rozenberg and A. Salomaa (Eds.) The book of L, Springer-Verlag, Berlin (1986) 298–307.
van Leeuwen, J., Tan, R.B.: Computer Network with Compact Routing Tables. In: G. Rozenberg and A. Salomaa (Eds.), The Book of L., Springer-Verlag, Berlin (1986) 259–273.
Ružička, P.: A Note on the Efficiency of an Interval Routing Algorithm. The Computer Journal 34 (1991) 475–476.
Santoro, N., Khatib, R.: Routing Without Routing Tables. Tech. Rep. SCS-TR-6, School of Computer Science, Carleton University (1982). Also as: Labeling and Implicit Routing in Networks. The Computer Journal 28 (1) (1985) 5–8.
Santoro, N., Khatib, R.: Labeling and Implicit Routing in Networks. The Computer Journal, 28 (1) (1985) 5–8.
Tse, S. S.H., Lau, F. C.M.: A Lower Bound for Interval Routing in General Networks. Tech. Rep. TR-94-09, Department of Computer Science, University of Hong Kong (1994).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Eilam, T., Moran, S., Zaks, S. (1996). A lower bound for Linear Interval Routing. In: Babaoğlu, Ö., Marzullo, K. (eds) Distributed Algorithms. WDAG 1996. Lecture Notes in Computer Science, vol 1151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61769-8_13
Download citation
DOI: https://doi.org/10.1007/3-540-61769-8_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61769-3
Online ISBN: 978-3-540-70679-3
eBook Packages: Springer Book Archive