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Hot-Potato Algorithms for Permutation Routing
November 1995 (vol. 6 no. 11)
pp. 1168-1176

Abstract—We develop a methodology for the design of hot-potato algorithms for routing permutations. The basic idea is to convert existing store-and-forward routing algorithms to hot-potato algorithms. Using it, we obtain the following complexity bounds for permutation routing:n×n Mesh: 7n+o(n) steps. • 2n hypercube: O(n2) steps. •n×n Torus: 4n+o(n) steps.The algorithm for the two-dimensional grid is the first to be both deterministic and asymptotically optimal. The algorithm for the 2n-nodes Boolean cube is the first deterministic algorithm that achieves a complexity of o(2n) steps.

[1] A.S. Acampora and S.I.A. Shah, "Multihop Lightwave Networks: A Comparison of Store-and-Forward and Hot-Potato Routing," Proc. IEEE INFOCOM, pp. 10-19. IEEE CS Press, 1991.
[2] P. Baran, "On Distributed Communication Networks," IEEE Trans. Comm. Systems, vol. 12, nos. 1-2, pp. 1-9, Mar. 1964.
[3] K. Batcher,“Sorting networks and their applications,” Proc. AFIPS Spring Joint Computing Conf., vol. 32, pp. 307-314, 1968.
[4] A. Borodin and J.E. Hopcroft,"Routing, merging and sorting on parallel models of comparison," J. Computer and System Science, vol. 30, pp. 130-145, 1985.
[5] A. Bendor,S. Halevi,, and A. Schuster,“On greedy hot-potatoe routing,” Technical Report LPCR #9204, CS Dept., Technion, Jan. 1993.
[6] A. Bar-Noy, B. Schieber, P. Raghavan, and H. Tamaki, "Fast Deflection Routing for Packets and Worms," Proc. 12th Ann. ACM Sump. Principles of Distributed Computing (PODC 93), pp. 75-86,Ithaca, N.Y., Aug. 1993.
[7] U. Feige and P. Raghavan, "Exact Analysis of Hot Potato Routing. 33rd Ann. Symp. Foundations of Computer Science, pp. 553-562, Oct. 1992.
[8] A.G. Greenberg and J. Goodman, "Sharp Approximate Models of Adaptive Routing in Mesh Networks," Teletraffic Analysis and Computer Performance Evaluation, J.W. Cohen, O.J. Boxma, and H.C. Tijms, eds., pp. 255-270.Amsterdam: Elsevier, 1988.
[9] A.G. Greenberg and B. Hajek, "Deflection Routing in Hypercube Networks," IEEE Trans. Comm., vol. 35, no. 6, pp. 1,070-1,081, June 1992.
[10] N. Haberman,“Parallel neighbor-sort (or the glory of the induction principle),” Technical Report AD-759248, Nat’l Technical Information Service, U.S. Dept. of Commerce, 1972.
[11] B. Hajek,“Bounds on evacuation time for deflection routing,” Distributed Computing, vol. 5, pp. 1-6, 1991.
[12] W.D. Hillis, The Connection Machine, MIT Press, Cambridge, Mass., 1985.
[13] C. Kaklamanis, D. Krizanc, and S. Rao, "Hot Potato Routing on Processor Arrays," Proc. Fifth Symp. Parallel Algorithms and Architectures, pp. 273-282, 1993.
[14] M. Kaufmann, H. Lauer, and H. Schroder, "Fast Deterministic Hot-Potato Routing on Processor Arrays," Proc. Fifth Int'l Symp. Algorithms and Computation ISAAC '94, D.Z. Du and X.S. Zhang, eds., LNCS 834, pp. 333-341,Beijing, Aug. 1994.
[15] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[16] D.H. Lawrie and D.A. Padua,“Analysis of message switching with shuffle-exchanges in multi-processors,” Interconnection Networks, 1984.
[17] N.F. Maxemchuk, "Comparison of Deflection and Store-and-Forward Techniques in the Manhattan Street and Shuffle-Exchange Networks," Proc. INFORCOM '89, vol. 3, pp. 800-809, Apr. 1989.
[18] I. Newman and A. Schuster,“Hot-potato algorithms for permutation routing,” Technical Report LPCR #9201, CS Dept., Technion, Nov. 1992.
[19] G. Plaxton,“Load balancing, selection and sorting on the hypercube,” Proc. ACM Symp. Parallel Algorithms and Architectures, pp. 64-73, June 1989.
[20] R. Prager,“An algorithm for routing in hypercube networks,” PhD thesis, Univ. of Toronto, 1986.
[21] C.L. Seitz,“The Caltech Mosaic C: An experimental, fine-grain multicomputer,” Fourth Ann. ACM Symp. Parallel Algorithms and Architectures, keynote speech, San Diego, June 1992.
[22] B. Smith,“Architecture and applications of the HEP multiprocessor computer system,” Proc. (SPIE) Real Time Signal Processing IV, pp. 241-248, 1981.
[23] C. Schnorr and A. Shamir,“An optimal sorting algorithm for mesh connected computers,”inProc. 18th ACM Symp. on Theory of Comput., 1986, pp. 263–271.
[24] T. Syzmanski,“An analysis of hot-potato routing in a fiber-optic packet switched hypercube,” IEEE INFOCOM’90 Proc., vol. 1, pp. 918-925, June 1990.
[25] Z. Zhang and A.S. Acampora, "Performance Analysis of Multihop Lightwave Networks with Hot Potato Routing and Distance Age Priorities," Proc. IEEE INFOCOM, pp. 1,012-1,021. IEEE CS Press, 1991.

Index Terms:
Deflection routing, packet routing, parallel algorithms.
Ilan Newman, Assaf Schuster, "Hot-Potato Algorithms for Permutation Routing," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 11, pp. 1168-1176, Nov. 1995, doi:10.1109/71.476188
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