Routing with bounded buffers and hot-potato routing in vertex-symmetric networks
O(log n · D), with high probability (w.h.p.), if constant size buffers are available for each edge,
O(log n · Dlog1+∈D) for any ε > 0, w.h.p., if for each vertex buffers of size 3, independent of the degree of the network, are available.
The schedule for the second result can be converted into a hot-potato routing schedule, if a self-loop is added to each vertex.
E.g., for any bounded degree vertex-symmetric network with self-loops and diameter O(log n) (among them expanders) we obtain a hot-potato routing protocol that needs time O(log2n(log log n)1+∈) for any ε > 0 to route a randomly chosen function and any permutation, w.h.p.
Our protocols also allow bounds on the space requirements for vertices and packets in the network: we show that O(D(log log D+log d)) space suffices for storing routing information in the vertices and O(log D) space suffices for storing routing information in the packets.
This is the first result about space-efficient routing where both the buffer size and the space for storing routing information is strongly bounded. Previous results are only known about routing protocols that either can reduce the buffer size or the space for storing routing information. For space-efficient hot-potato routing no general results are known.
In order to prove the results above we introduce a new off-line routing protocol for arbitrary networks which is fast even for vertex buffers of size 1. This bound can not be reached by any other non-trivial off-line routing protocol yet.
KeywordsBuffer Size Output Buffer Arbitrary Network Path System Local Lemma
Unable to display preview. Download preview PDF.
- [AES92]N. Alon, P. Erdős, J. Spencer. The Probabilistic Method. Wiley Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, 1992.Google Scholar
- [AS92]A. Acampora, S. Shah. Multihop Lightwave Networks: a Comparison of Store-and-Forward and Hot-Potato Routing. IEEE Transaction on Communications, pp. 1082–1090, 1992.Google Scholar
- [FR92]U. Feige, P. Raghavan. Exact Analysis of Hot-Potato Routing. In Proc. of the 33rd Symp. on Foundations of Computer Science, pp. 553–562, 1992.Google Scholar
- [GH92]A. Greenberg, B. Hajek. Deflection Routing in Hypercube Networks. IEEE Transactions on Communications, pp. 1070–1081, 1992.Google Scholar
- [L92]F.T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann, San Mateo, CA, 1992.Google Scholar
- [LMR88]F.T. Leighton, B.M. Maggs, S.B. Rao. Universal Packet Routing Algorithms. In Proc. of the 29th Ann. Symp. on Foudations of Computer Science, pp. 256–271, 1988.Google Scholar
- [LR88]F.T. Leighton, S.B. Rao. An Approximate Max-Flow Min-Cut Theorem for Uniform Multicommodity Flow Problems with Applications to Approximation Algorithms. In Proc. of the 29th Ann. Symp. on Foudations of Computer Science, pp. 422–431, 1988.Google Scholar
- [M89]N. Maxemchuk. Comparison of Deflection and Store-and-Forward Techniques in the Manhattan Street and Shuffle-Exchange Networks. In Proc. of the IEEE INFOCOM, pp. 800–809, 1989.Google Scholar
- [M94]M. Morgenstern. Existence and Explicit Constructions of q + 1 Regular Ramanujan Graphs for Every Prime Power q. Journal of Comb. Theory, Series B 62, pp. 44–62, 1994.Google Scholar
- [MS95]F. Meyer auf der Heide, C. Scheideler. Space-Efficient Routing in Vertex-Symmetric Networks. To appear at SPAA 95.Google Scholar
- [MV95]F. Meyer auf der Heide, B. Vöcking. A Packet Routing Protocol for Arbitrary Networks. In Proc. of the 12th Symp. on Theoretical Aspects of Computer Science, pp. 291–302, 1995.Google Scholar
- [MW95]F. Meyer auf der Heide, M. Westermann. Hot-Potato Routing on Multi-Dimensional Tori. To appear at WG95 (21st Workshop on Graph-Theoretical Concepts in Computer Science), June 1995.Google Scholar
- [R91]A.G. Ranade. How to Emulate Shared Memory. Journal of Computer and System Sciences 42, pp. 307–326, 1991.Google Scholar
- [S90]T. Szymanski. An Analysis of Hot-Potato Routing in a Fiber Optic Packet Switched Hypercube. In Proc. of the IEEE INFOCOM, pp. 918–925, 1990.Google Scholar
- [U92]E. Upfal. An O(log N) Deterministic Packet Routing Scheme. Journal of the ACM 39, 1992.Google Scholar