Abstract
We consider the problem of finding a short path between any two nodes of a network when no global information is available, nor any oracle to help in routing. A mobile agent, situated in a starting node, has to walk to a target node traversing a path of minimum length. All information about adjacencies is distributed to certain nodes called landmarks. We wish to minimize the total memory requirements as well as keep the memory requirements per landmark to reasonable levels. We propose a landmark selection and information distribution scheme with overall memory requirement linear in the number of nodes, and constant memory consumption per non-landmark node. We prove that a navigation algorithm using this scheme attains a constant stretch factor overhead in tree topologies, compared to an optimal landmark-based routing algorithm that obeys certain restrictions. The flexibility of our approach allows for various trade-offs, such as between the number of landmarks and the size of the region assigned to each landmark.
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
Abraham, I., Gavoille, C., Malkhi, D.: On space-stretch trade-offs for compact routing schemes. Research Report RR-1374-05, LaBRI, France (November 2005)
Abraham, I., Gavoille, C., Malkhi, D.: Compact routing for graphs excluding a fixed minor. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 442–456. Springer, Heidelberg (2005)
Abraham, I., Malkhi, D.: Name Independent Routing for Growth Bounded Networks. In: Proc.17th ACM Symp. Parall. Algorithms and Architectures (SPAA 2005), pp. 49–55 (2005)
Awerbuch, B., Bar-Noy, A., Linial, N., Peleg, D.: Compact distributed data structures for adaptive network routing. In: Proc. of 21st ACM Symp. on Theory of Computing, pp. 230–240 (May 1989)
Bar-Ilan, J., Kortsarz, G., Peleg, D.: How to allocate network centers. J. Algorithms 15, 385–415 (1993)
Buhrman, H., Hoepman, J.-H., Vitanyi, P.: Optimal routing tables. In: Proc. 15th ACM Symp. on Principles of Distributed Computing, pp. 134–142 (May 1996)
Fang, Q., Gao, J., Guibas, L., de Silva, V., Zhang, L.: GLIDER: Gradient Landmark- Based Distributed Routing for Sensor Networks. In: Proc. 24th Conf. of IEEE Com. Soc. (INFOCOM 2005) (2005)
Fraigniaud, P., Gavoille, C.: Memory requirement for universal routing schemes. In: Proc. 14th ACM Symp. on Principles of Distributed Computing, pp. 223–230 (August 1995)
Fraigniaud, P., Gavoille, C.: Local memory requirement of universal routing schemes. In: Proc. 8th ACM Symp. on Parallel Algorithms and Architectures, pp. 183–188 (June 1996)
Frederickson, G.N., Janardan, R.: Separator-Based Strategies for Efficient Message Routing. In: Proc. 27th IEEE Symp. on Foundations of Computer Science, pp. 428–437 (1986)
Frederickson, G.N., Janardan, R.: Designing networks with compact routing tables. Algorithmica 3, 171–190 (1988)
Frederickson, G.N., Janardan, R.: Efficient message routing in planar networks. SIAM Journal on Computing 18, 843–857 (1989)
Fraigniaud, P., Gavoille, C.: Routing in Trees. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 757–772. Springer, Heidelberg (2001)
Gavoille, C., Gengler, M.: Space-efficiency of routing schemes of stretch factor three. In: Proc. 4th Int. Colloq. on Structural Information & Communication Complexity, pp. 162–175. Carleton Scientific (1997)
Gavoille, C., Peleg, D.: Compact and localized distributed data structures. Distributed Computing 16(2-3), 111–120 (2003)
Gavoille, C., Perennes, S.: Memory requirement for routing in distributed networks. In: Proc. 15th ACM Symp. on Principles of Distributed Computing, pp. 125–133 (May 1996)
Hochbaum, D., Shmoys, D.B.: A best possible heuristic for the k −center problem. Mathematics of Operations Research 10, 180–184 (1985)
Khuller, S., Raghavachari, B., Rosenfeld, A.: Landmarks in Graphs. Discrete Applied Mathematics 70(3), 217–229 (1996)
Khuller, S., Sussmann, Y.J.: The capacitated k-center problem. SIAM J. Discrete Math. 13, 403–418 (2000)
Kleinrock, L., Kamoun, F.: Hierarchical routing for large networks: performance evaluation and optimization. Computer Networks 1, 155–174 (1977)
Kleinrock, L., Kamoun, F.: Optimal clustering structures for hierarchical topological design of large computer networks. Computer Networks 10, 221–248 (1980)
Kranakis, E., Krizanc, D.: Lower bounds for compact routing. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 529–540. Springer, Heidelberg (1996)
Peleg, D.: Distance-dependent distributed directories. Information and Computation, pp. 270–298 (1993)
Peleg, D., Upfal, E.: A tradeoff between size and efficiency for routing tables. J. ACM 36, 510–530 (1989)
Perlman, R.: Hierarchical networks and the subnetwork partition problem. In: Proc. 5th Conf. on System Sciences (1982)
Santoro, N., Khatib, R.: Labelling and implicit routing in networks. The Computer Journal 28, 5–8 (1985)
Thorup, M., Zwick, U.: Compact routing schemes. In: Proc. 13th annual ACM symposium on Parallel algorithms and architectures, pp. 1–10, Crete Island, Greece (2001)
Tsuchiya, P.F.: The landmark hierarchy: A new hierarchy for routing in very large networks. Computer Communication Review 18(4), 35–42 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Emiris, I.Z., Markou, E., Pagourtzis, A. (2006). Distributed Routing in Tree Networks with Few Landmarks. In: Erlebach, T. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2006. Lecture Notes in Computer Science, vol 4235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11922377_5
Download citation
DOI: https://doi.org/10.1007/11922377_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-48822-4
Online ISBN: 978-3-540-48824-8
eBook Packages: Computer ScienceComputer Science (R0)