Compact routing schemes

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Compact routing schemes

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ACM Symposium on Parallel Algorithms and Architectures archive
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures table of contents

Crete Island, Greece

Pages: 1 - 10

Year of Publication: 2001

ISBN:1-58113-409-6

Authors

Mikkel Thorup	AT&T Labs - Research, 180 Park Avenue, Florham Park, NJ
Uri Zwick	School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGARCH: ACM Special Interest Group on Computer Architecture

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 17, Downloads (12 Months): 184, Citation Count: 61

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ABSTRACT

We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extremely short. The routing decision at each node takes constant time. Yet, the stretch of these routing schemes, i.e., the worst ratio between the cost of the path on which a packet is routed and the cost of the cheapest path from source to destination, is a small constant. Our schemes achieve a near-optimal tradeoff between the size of the routing tables used and the resulting stretch. More specifically, we obtain:

A routing scheme that uses only O (n ^1/2) bits of memory at each node of an n-node network that has stretch 3. The space is optimal, up to logarithmic factors, in the sense that every routing scheme with stretch < 3 must use, on some networks, routing tables of total size &OHgr;(n²), and every routing scheme with stretch < 5 must use, on some networks, routing tables of total size &OHgr;(n^3/2). The headers used are only (1 + &Ogr;(1)) log²> n-bits long and each routing decision takes constant time. A variant of this scheme with [log2 n] -bit headers makes routing decisions in &Ogr;(log log n) time.
Also, for every integer k > 2, a general handshaking based routing scheme that uses O (n^1/k) bits of memory at each node that has stretch 2k - 1. A conjecture of Erdös from 1963, settled for k = 3, 5, implies that the routing tables are of near-optimal size relative to the stretch. The handshaking is similar in spirit to a DNS lookup in TCP/IP. Headers are &Ogr;(log² n) bits long and each routing decision takes constant time. Without handshaking, the stretch of the scheme increases to 4k — 5. One ingredient used to obtain the routing schemes mentioned above, may be of independent practical and theoretical interest:
A shortest path routing scheme for trees of arbitrary degree and diameter that assigns each vertex of an n-node tree a (1 + &Ogr;(1)) log² n-bit label. Given the label of a source node and the label of a destination it is possible to compute, in constant time, the port number of the edge from the source that heads in the direction of the destination.

The general scheme for k > 2 also uses a clustering technique introduced recently by the authors. The clusters obtained using this technique induce a sparse and low stretch tree cover of the network. This essentially reduces routing in general networks into routing problems in trees that could be solved using the above technique.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Serge Abiteboul , Haim Kaplan , Tova Milo, Compact labeling schemes for ancestor queries, Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, p.547-556, January 07-09, 2001, Washington, D.C., United States
	2	N. Alon and M. Naor. Derandomization, witnesses for boolean matrix multiplication, and construction of perfect hash functions. Algorithmica, 16:434-449, 1996.
	3	S. Alstrup. Personal communication, SODA 2001.
	4	Baruch Awerbuch , Amotz Bar Noy , Nathan Linial , David Peleg, Improved routing strategies with succinct tables, Journal of Algorithms, v.11 n.3, p.307-341, Sep. 1990 [doi>10.1016/0196-6774(90)90017-9]
	5	Baruch Awerbuch , David Peleg, Routing with polynomial communication-space trade-off, SIAM Journal on Discrete Mathematics, v.5 n.2, p.151-162, May 1992 [doi>10.1137/0405013]
	6	Paul Beame , Faith E. Fich, Optimal bounds for the predecessor problem, Proceedings of the thirty-first annual ACM symposium on Theory of computing, p.295-304, May 01-04, 1999, Atlanta, Georgia, United States [doi>10.1145/301250.301323]
	7	Thomas M. Cover , Joy A. Thomas, Elements of information theory, Wiley-Interscience, New York, NY, 1991
	8	Lenore J. Cowen, Compact routing with minimum stretch, Journal of Algorithms, v.38 n.1, p.170-183, Jan. 2001 [doi>10.1006/jagm.2000.1134]
	9	S. Deering and R. Hinden. Internet protocol, version 6 (IPv6), specification. Network Working Group, Request for Comments: 2460, ftp://ftp.ipv6.org/pub/rfc/rfc2460.txt, December 1998.
	10	Dorit Dor , Shay Halperin , Uri Zwick, All-Pairs Almost Shortest Paths, SIAM Journal on Computing, v.29 n.5, p.1740-1759, March 2000 [doi>10.1137/S0097539797327908]
	11	Tamar Eilam , Cyril Gavoille , David Peleg, Compact routing schemes with low stretch factor (extended abstract), Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing, p.11-20, June 28-July 02, 1998, Puerto Vallarta, Mexico [doi>10.1145/277697.277702]
	12	P. Erdos. Extremal problems in graph theory. In Theory of Graphs and its Applications (Proc. Sympos. Smolenice, 1963), pages 29-36. Publ. House Czechoslovak Acad. Sci., Prague, 1964.
	13	Michalis Faloutsos , Petros Faloutsos , Christos Faloutsos, On power-law relationships of the Internet topology, Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication, p.251-262, August 30-September 03, 1999, Cambridge, Massachusetts, United States
	14	Pierre Fraigniaud , Cyril Gavoille, Memory requirement for universal routing schemes, Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing, p.223-230, August 20-23, 1995, Ottowa, Ontario, Canada [doi>10.1145/224964.224989]
	15	P. Fraigniaud and C. Gavoille. Interval routing schemes. Algorithmica, 21(2):155-182, 1998.
	16	Michael L. Fredman , János Komlós , Endre Szemerédi, Storing a Sparse Table with 0(1) Worst Case Access Time, Journal of the ACM (JACM), v.31 n.3, p.538-544, July 1984 [doi>10.1145/828.1884]
	17	Cyril Gavoille, A survey on interval routing, Theoretical Computer Science, v.245 n.2, p.217-253, Aug. 28, 2000 [doi>10.1016/S0304-3975(99)00283-2]
	18	C. Gavoille. Personal communication at SODA, 2001.
	19	Cyril Gavoille , Marc Gengler, Space-efficiency for routing schemes of stretch factor three, Journal of Parallel and Distributed Computing, v.61 n.5, p.679-687, May 2001 [doi>10.1006/jpdc.2000.1705]
	20	Cyril Gavoille , Stéphane Pérennès, Memory requirement for routing in distributed networks, Proceedings of the fifteenth annual ACM symposium on Principles of distributed computing, p.125-133, May 23-26, 1996, Philadelphia, Pennsylvania, United States [doi>10.1145/248052.248075]
	21	Brian W. Kernighan , Dennis M. Ritchie, The C programming language, Prentice Hall Press, Upper Saddle River, NJ, 1989
	22	David Peleg, Distributed computing: a locality-sensitive approach, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2000
	23	David Peleg , Eli Upfal, A trade-off between space and efficiency for routing tables, Journal of the ACM (JACM), v.36 n.3, p.510-530, July 1989 [doi>10.1145/65950.65953]
	24	N. Santoro and R. Khatib. Labelling and implicit routing in networks. The Computer Journal, 28(1):5-8, 1985.
	25	Mikkel Thorup , Uri Zwick, Approximate distance oracles, Proceedings of the thirty-third annual ACM symposium on Theory of computing, p.183-192, July 2001, Hersonissos, Greece [doi>10.1145/380752.380798]
	26	P. van Emde Boas. Preserving order in a forest in less than logarithmic time and linear space. Information Processing Letters, 6(3):80-82, 1977.
	27	P. van Emde Boas, R. Kaas, and E. Zijlstra. Design and implementation of an efficient priority queue. Math. Syst. Theory, 10:99-127, 1977.
	28	J. van Leeuwen and R. Tan. Computer networks with compact routing tables. In G. Rozemberg and A. Salomaa, editors, The book of L, pages 259-273. Springer-Verlag, 1986.

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	Haim Kaplan , Tova Milo , Ronen Shabo, A comparison of labeling schemes for ancestor queries, Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms, p.954-963, January 06-08, 2002, San Francisco, California
	Marta Arias , Lenore J. Cowen , Kofi A. Laing , Rajmohan Rajaraman , Orjeta Taka, Compact routing with name independence, Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures, June 07-09, 2003, San Diego, California, USA
	Tamar Eilam , Cyril Gavoille , David Peleg, Compact routing schemes with low stretch factor, Journal of Algorithms, v.46 n.2, p.97-114, February 2003
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