Abstract
In contrast to classical offline k-k routing, the online packet routing problem allows for an arbitrary number of packets with arbitrary end points and release times. We study this problem on linear array and ring networks. We generalize an earlier result for the offline problem by showing that Farthest First (FF) scheduling is optimal with respect to makespan on linear arrays. We also show that two other algorithms (Longest in System (LIS) and Moving Priority (MP)) have competitive ratio 2 with respect to makespan on linear arrays. For bidirectional rings, we show that, the competitive ratio of shortest path routing combined with LIS or MP scheduling is in [2:5; 3) and the competitive ratio of shortest path routing combined with FF scheduling is 2. The latter algorithm is optimal among deterministic memoryless algorithms and all algorithms of which we are aware in the literature.
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References
M. Adler, A. L. Rosenberg, R. K. Sitaraman, and W. Unger. Scheduling time-constrained communication in linear networks. In Proc. ACM Symp. on Parallel Algorithms and Architectures, pages 269–278, 1998.
A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queuing theory. In Proc. ACM Symp. on Theory of Computing, pages 376–385, 1996.
I. Cidon, S. Kutten, Y. Mansour, and D. Peleg. Greedy packet scheduling. SIAM Journal on Computing, 24(1):148–157, 1995.
M. Kaufmann and J. F. Sibeyn. Deterministic routing on circular arrays. In Proc. IEEE Symp. on Parallel and Distributed Processing, pages 376–383, 1992.
M. Kaufmann and J. F. Sibeyn. Randomized multipacket routing an sorting on meshes. Algorithmica, 17:224–244, 1997.
K.-S. Lui and S. Zaks. Scheduling in synchronous networks and the greedy algorithm. In Proc. Int. Workshop on Distributed Algorithms, pages 66–80, 1997.
F. Makedon and A. Symvonis. Optimal algorithms for multipacket routing problems on rings. Journal of Parallel and Distributed Computing, 22(1):37–43, 1994.
Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. Journal of Algorithms, 14(3):449–465, 1993.
W. Mao and R. Simha. Routing and scheduling file transfers in packet-switched networks. Journal of Computing and Information, 1(1):559–574, 1994.
P. I. Rivera-Vega, R. Varadarajan, and S. B. Navathe. Scheduling data redistribution in distributed databases. In Proc. IEEE Int. Conf. on Data Engineering, pages 166–173, 1990.
J. F. Sibeyn. Deterministic routing and sorting on rings. In Proc. IEEE Int. Parallel Processing Symp., pages 406–410, 1994.
L. G. Valiant and G. J. Brebner. Universal schemes for parallel communication. In Proc. ACM Symp. on Theory of Computing, pages 263–277, 1981.
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Havill, J.T. (2001). Online Packet Routing on Linear Arrays and Rings. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_63
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DOI: https://doi.org/10.1007/3-540-48224-5_63
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