Abstract
We prove bounds for the length of optimal schedules for store-and-forward packet routing in the setting of arbitrary bandwidths and transit times. The problem is commonly studied only in the setting of unit bandwidths and unit transit times. Our results generalize the existing work to a much broader class of instances and also improve the known bounds significantly. For the case of unit transit times and bandwidths we improve the best known bound of 39(C + D) to 23.4(C + D), where C and D denote the trivial lower bounds congestion and dilation. If every link in the network has a certain minimum transit time or capacity our bounds improve even further up to 4.32(C + D). Key to our results is a framework which employs tight bounds for instances where each packet travels along only a small number of edges. Further insights for such instances would reduce our constants even more. This is the first improvement of the bounds for this very fundamental problem in more than 10 years.
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References
Adler, M., Khanna, S., Rajaraman, R., Rosén, A.: Time-constrained scheduling of weighted packets on trees and meshes. Algorithmica 36, 123–152 (2003)
Adler, M., Sitaraman, R., Rosenberg, A., Unger, W.: Scheduling time-constrained communication in linear networks. In: Proceedings of the 10th annual ACM symposium on Parallel Algorithms and Architectures (SPAA 1998), pp. 269–278 (1998)
Busch, C., Magdon-Ismail, M., Mavronicolas, M., Spirakis, P.: Direct routing: Algorithms and complexity. Algorithmica 45, 45–68 (2006)
di Ianni, M.: Efficient delay routing. Theoretical Computer Science 196, 131–151 (1998)
Fleischer, L., Skutella, M.: Minimum cost flows over time without intermediate storage. In: Proceedings of the 14th Annual Symposium on Discrete Algorithms, SODA 2003 (2003)
Fleischer, L., Skutella, M.: Quickest flows over time. SIAM Journal on Computing 36, 1600–1630 (2007)
Hall, A., Hippler, S., Skutella, M.: Multicommodity flows over time: Efficient algorithms and complexity. Theoretical Computer Science 2719, 397–409 (2003)
Hall, A., Langkau, K., Skutella, M.: An FPTAS for quickest multicommodity flows with inflow-dependent transit times. Algorithmica 47, 299–321 (2007)
Meyer Auf Der Heide, F., Vocking, B.: Shortest paths routing in arbitrary networks. Journal of Algorithms 31, 105–131 (1999)
Hoppe, B., Tardos, É.: The quickest transshipment problem. Mathematics of Operations Research 25, 36–62 (2000)
Koch, R., Peis, B., Skutella, M., Wiese, A.: Real-Time Message Routing and Scheduling. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX 2009. LNCS, vol. 5687, pp. 217–230. Springer, Heidelberg (2009)
Leighton, F.T., Maggs, B.M., Rao, S.B.: Packet routing and job-scheduling in O(congestion + dilation) steps. Combinatorica 14, 167–186 (1994)
Leighton, F.T., Maggs, B.M., Richa, A.W.: Fast algorithms for finding O(congestion + dilation) packet routing schedules. Combinatorica 19, 375–401 (1999)
Leighton, F.T., Makedon, F., Tollis, I.G.: A 2n − 2 step algorithm for routing in an n ×n array with constant size queues. In: Proceedings of the 1st Annual Symposium on Parallel Algorithms and Architectures (SPAA 1989), pp. 328–335 (1989)
Leung, J.Y.-T.: Handbook of Scheduling: Algorithms, Models and Performance Analysis. CRC Press, Inc., Boca Raton (2004)
Mansour, Y., Patt-Shamir, B.: Many-to-one packet routing on grids. In: Proceedings of the 27th Annual Symposium on Theory of Computing (STOC 1995), pp. 258–267 (1995)
Ostrovsky, R., Rabani, Y.: Universal O(congestion + dilation + log1 + ε N) local control packet switching algorithms. In: Proceedings of the 29th annual ACM Symposium on Theory of Computing (STOC 1997), pp. 644–653 (1997)
Erdős, P., Lovász, L.: Problems and results on 3-chromatic hypergraphs and some related questions. In: Infinite and Finite Sets Colloq. Math. Soc. Janos Bolyai, vol. 11, pp. 609–627. North-Holland, Amsterdam (1975)
Peis, B., Skutella, M., Wiese, A.: Packet routing: Complexity and algorithms. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 217–228. Springer, Heidelberg (2010)
Peis, B., Skutella, M., Wiese, A.: Packet routing on the grid. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 120–130. Springer, Heidelberg (2010)
Peis, B., Wiese, A.: Universal packet routing with arbitrary bandwidths and transit times. Technical Report 024-2010, Technische Universität Berlin (November 2010)
Rabani, Y., Tardos, É.: Distributed packet switching in arbitrary networks. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC 1996), pp. 366–375. ACM, New York (1996)
Rajasekaran, S.: Randomized algorithms for packet routing on the mesh. Technical Report MS-CIS-91-92, Dept. of Computer and Information Sciences, Univ. of Pennsylvania, Philadelphia, PA (1991)
Scheideler, C.: Universal Routing Strategies for Interconnection Networks. LNCS, vol. 1390, pp. 57–71 (1998)
Srinivasan, A., Teo, C.-P.: A constant-factor approximation algorithm for packet routing and balancing local vs. global criteria. SIAM Journal on Computing 30 (2001)
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Peis, B., Wiese, A. (2011). Universal Packet Routing with Arbitrary Bandwidths and Transit Times. In: Günlük, O., Woeginger, G.J. (eds) Integer Programming and Combinatoral Optimization. IPCO 2011. Lecture Notes in Computer Science, vol 6655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20807-2_29
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DOI: https://doi.org/10.1007/978-3-642-20807-2_29
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