Abstract
We study the source routing problem on √N x √N tori and meshes. In this problem, the paths for packets are the shortest ones. And the routing decision is distributed in a way that the path designated to a packet is determined entirely on its source node, with no knowledge of the other packets injected to other nodes and the system load distribution. The cost we concern about is the maximum load among the edges. We use competitive analysis to measure the performance of algorithms. We show that the competitive ratio for any algorithm is ,Ω(log N), and we provide an algorithm whose competitive ratio is O(log N).
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N. Alon, G. Kalai, M. Ricklin, and L. Stockmeyer. Lower bounds on the competitive ratio for mobile user tracking and distributed job scheduling. In 33rd FOCS, pages 334–343, 992.
B. Awerbuch, Y. Azar, and S. Plotkin. Throughput-competitive online routing. In 34th FOGS, pages 32–40, 1993.
B. Awerbuch, Y. Bartal, and A. Fiat. Competitive distributed file allocation. In 25th STOC, pages 164–173, 1993.
B. Awerbuch, Y. Bartal, A. Fiat, and A. Rosen. Competitive non-preemptive call control. In 5th SODA, pages 312–320, 1994.
B. Awerbuch, R. Gawlick, T. Leighton, and Y. Rabani. On-line admission control and circuit routing for high performance computing and communication. In 35th FOCS, pages 412–423, 1994.
B. Awerbuch, S. Kutten, and D. Peleg. Competitive distributed job scheduling. In 24th STOC, pages 517–580, 1992.
Y. Bartal, A. Fiat, and Y. Rabani. Competitive algorithms for distributed data management. In 24th STOC, pages 39–50, 1992.
Y. Banal and A. Rosén. The distributed k-server problem — a competitive distributed translator for k-server algorithms. In 33rd FOGS, pages 344–353, 1992.
A. Borodin, P. Raghavan, B. Schieber, and E. Upfal. How much can hardware help routing. In 25th STOC, pages 573–582, 1993.
S. Irani, N. Reingold, J. Westbrook, and D. Sleator. Randomized competitive algorithms for the list update problem. In 2nd SODA, pages 251–260, 1991.
C. Kaklamanis, D. Krizanc, and T. Tsantilas. Tight bounds for oblivious routing in the hypercube. In 2nd SPAA, pages 31–36, 1990.
E. Koutsoupias and C. Papadimitriou. On the k-server conjecture. In 26th STOC, pages 507–511, 1994.
M. Kunde. Packet routing on grids of processors. Algorithmica, 9(1):32–46, 1993.
T. Leighton. Average case analysis of greedy routing algorithms on arrays. In 2nd SPAA, pages 2–10, 1990.
T. Leighton, F. Makedon, and I. Tollis. A 2n −2 step algorithm for routing in an nx n array with constant size queues. In 1st SPAA, pages 328–335, 1989.
S. Rajasekaran and R. Overholt. Constant queue routing on a mesh. In 8th Annual Symposium on Theoretical Aspects of Computer Science, volume 480 of Lecture Nodes in Computer Science, pages 444–455, Springer-Verlag, 1991.
J. Sibeyn, B. Chlebus, and M. Kaufmann. Deterministic permutation routing on meshes. J. Algorithms, 22:111–141, 1997.
D. Sleator and R. Tarjan. Amortized efficiency of list update and paging rules. Comm. ACM, 28:202–208, 1985.
S. Vishwanathan. Randomized on-line graph coloring. J. Algorithms, 13(4):657–669, 1992.
T.-H. Yeh, C.-M. Kuo, C.-L. Lei, and H.-C. Yen. Competitive source routing on tori and meshes. Technical report, Dept. of Electrical Engineering, National Taiwan University, 1996.
N. Young. The k-server dual and loose competitiveness for paging. Algorithmica, 11(6):525–541, 1994.
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© 1997 Springer-Verlag Berlin Heidelberg
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Yeh, TH., Kuo, hM., Lei, CL., Yen, HC. (1997). Competitive source routing on tori and meshes. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_10
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DOI: https://doi.org/10.1007/3-540-63890-3_10
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