In this paper, the problem of routing messages along shortest paths in a distributed network without using complete routing tables is considered. In particular, we first study the complexity of deriving minimum (in terms of number of intervals) Interval Routing schemes, proving the NP-completeness of such a problem and giving an approximation algorithm for it. Next, we propose a different routing model and show how it can be applied to improve the space requirements of representing shortest paths among all pairs of nodes for some specific network topologies. Networks considered are paths, rings, trees, hypercubes, different types of d-dimensional grids, complete graphs and complete bipartite graphs. We show that such an approach behaves strictly better than the classical Interval Routing Scheme in terms of classes of graphs which can be efficiently handled and of global knowledge mantained at each node. In particular, for all the above cases optimal representations are given. Moreover, we show that Boolean Routing is more powerful than any intervalbased routing scheme: this is done by showing that any such a scheme (on any graph) can be efficiently simulated by Boolean Routing.
KeywordsDistributed systems compact routing tables interval routing NP-completeness shortest paths representation
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- 1.Y. Afek, E. Gafni, M. Ricklin. Upper and lower bounds for routing schemes in dynamic networks. Proc. 30th Symp. on Foundations of Computer Science, pp. 370–375,1989.Google Scholar
- 2.B. Awerbuch, A. Bar-Noy, N. Linial, D. Peleg. Compact distributed data structures for adaptive routing. Proc. 21st ACM Symp. on Theory of Computing, pp. 479–489,1989.Google Scholar
- 3.B. Awerbuch, A. Bar-Noy, N. Linial, D. Peleg. Improved routing strategies with succinct tables. Journal of Algorithms, 11, pp. 307–341,1990.Google Scholar
- 4.E. Bakker, J. van Leeuwen, R. Tan. Linear interval routing. Algorithms review, 2, 2, pp. 45–61, 1991.Google Scholar
- 5.N. Christofides. Worst case analysis of a new heuristic for the travelling salesman problem. Report No. 388, GSIA, Carnegie-Mellon University, Pittsburgh, PA, 1976.Google Scholar
- 6.G.N. Frederickson, R. Janardan. Designing networks with compact routing tables. Algorithmica, 3, pp. 171–190, 1988.Google Scholar
- 7.G.N. Frederickson, R. Janardan. Efficient message routing in planar networks. SIAM Journal on Computing, 18, pp. 843–857, 1989.Google Scholar
- 8.G.N. Frederickson, R. Janardan. Space efficient message routing in c-decomposable networks. SIAM Journal on Computing, 19, pp. 164–181, 1990.Google Scholar
- 9.M.R. Garey, D.S. Johnson. Computers and Intractability. A guide to the theory of NP-completeness. W.H. Freeman, San Francisco, 1979.Google Scholar
- 10.D. Peleg, E. Upfal. A trade-off between space and efficiency for routing tables. Journal of the ACM, 36, 3, pp. 510–530, 1989.Google Scholar
- 11.M. Santoro, R. Khatib. Labelling and implicit routing in networks. The Computer Journal, 28, pp. 5–8, 1985.Google Scholar
- 12.J. van Leeuwen, R.B. Tan. Routing with compact routing tables. In “The book of L”, G.Rozemberg and A.Salomaa eds., Springer-Verlag, pp. 259–273, 1986.Google Scholar
- 13.J. van Leeuwen, R.B. Tan. Interval routing. The Computer Journal, 30, pp. 298–307, 1987.Google Scholar