Abstract
We study dynamic routing in store-and-forward packet networks where each network link has bounded buffer capacity for receiving incoming packets and is capable of transmitting a fixed number of packets per unit of time. At any moment in time, packets are injected at various network nodes with each packet specifying its destination node. The goal is to maximize the throughput, defined as the number of packets delivered to their destinations.
In this paper, we make some progress on throughput maximization in various network topologies. Let n and m denote the number of nodes and links in the network, respectively. For line networks, we show that Nearest-to-Go (NTG), a natural distributed greedy algorithm, is \(\tilde{O}(\sqrt{n})\) -competitive, essentially matching a known \(\Omega(\sqrt{n})\) lower bound on the performance of any greedy algorithm. We also show that if we allow the online routing algorithm to make centralized decisions, there is a randomized polylog(n)-competitive algorithm for line networks as well as for rooted tree networks, where each packet is destined for the root of the tree. For grid graphs, we show that NTG has a competitive ratio of \(\tilde{\Theta}(n^{2/3})\) while no greedy algorithm can achieve a ratio better than \(\Omega(\sqrt{n})\) . Finally, for arbitrary network topologies, we show that NTG is \(\tilde{\Theta}(m)\) -competitive, improving upon an earlier bound of O(mn).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aiello, W., Ostrovsky, R., Kushilevitz, E., Rosén, A.: Dynamic routing on networks with fixed-size buffers. In: Proceedings of the 14th Anual ACM-SIAM Symposium on Discrete Algorithms, pp. 771–780. SIAM, Philadelphia (2003)
Kesselman, A., Mansour, Y., Lotker, Z., Patt-Shamir, B.: Buffer overflows of merging streams. In: Proceedings of the 15th Annual ACM Symposium on Parallel Algorithms, pp. 244–245. ACM Press, New York (2003)
Kothapalli, K., Scheideler, C.: Information gathering in adversarial systems: lines and cycles. In: Proceedings of the 15th Annual ACM Symposium on Parallel Algorithms, pp. 333–342 (2003)
Azar, Y., Zachut, R.: Packet routing and information gathering in lines, rings and trees. In: Proceedings of the 13th Annual European Symposium on Algorithms, pp. 484–495. Springer, New York (2005)
Labrador, M., Banerjee, S.: Packet dropping policies for ATM and IP networks. IEEE Commun. Surv. 2, 2–14 (1999)
Broder, A.Z., Frieze, A.M., Upfal, E.: A general approach to dynamic packet routing with bounded buffers. J. ACM 48, 324–349 (2001)
Broder, A., Upfal, E.: Dynamic deflection routing on arrays. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 348–355. ACM Press, New York (1996)
Mihail, M.: Conductance and convergence of markov chains—a combinatorial treatment of expanders. In: Proceedings of the 30th Annual IEEE Symposium on Fondations of Computer Science, pp. 526–531. IEEE, Philadelphia (1989)
Mitzenmacher, M.: Bounds on the greedy routing algorithm for array networks. J. Comput. Syst. Sci. 53, 317–327 (1996)
Stamoulis, G., Tsitsiklis, J.: The efficiency of greedy routing in hypercubes and butterflies. IEEE Trans. Commun. 42, 3051–3061 (1994)
Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., Williamson, D.P.: Adversarial queuing theory. J. ACM 48, 13–38 (2001)
Andrews, M., Awerbuch, B., Fernández, A., Leighton, T., Liu, Z., Kleinberg, J.: Universal-stability results and performance bounds for greedy contention-resolution protocols. J. ACM 48, 39–69 (2001)
Busch, C., Magdon-Ismail, M., Mavronicolas, M., Spirakis, P.G.: Direct routing: Algorithms and complexity. Algorithmica 45, 45–68 (2006)
Awerbuch, B., Azar, Y., Plotkin, S.: Throughput competitive on-line routing. In: Proceedings of the 34th Annual IEEE Symposium on Fondations of Computer Science, pp. 32–40. IEEE, Philadelphia (1993)
Scheideler, C., Vöcking, B.: Universal continuous routing strategies. In: Proceedings of the 8th Annual ACM Symposium on Parallel Algorithms, pp. 142–151. ACM Press, New York (1996)
Kesselman, A., Mansour, Y.: Harmonic buffer management policy for shared memory switches. Theor. Comput. Sci. 324, 161–182 (2004)
Lotker, Z., Patt-Shamir, B.: Nearly optimal FIFO buffer management for DiffServ. In: Proceedings of the 21th Annual ACM Symposium on Principles of Distributed Computing, pp. 134–143. ACM Press, New York (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
An extended abstract appeared in the Proceedings of the 8th Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005, Berkeley, CA, USA, pp. 1–13, Lecture Notes in Computer Science, vol. 1741, Springer, Berlin.
S. Angelov is supported in part by NSF Career Award CCR-0093117, NSF Award ITR 0205456 and NIGMS Award 1-P20-GM-6912-1.
S. Khanna is supported in part by an NSF Career Award CCR-0093117, NSF Award CCF-0429836, and a US-Israel Binational Science Foundation Grant.
K. Kunal is supported in part by an NSF Career Award CCR-0093117 and NSF Award CCF-0429836.
Rights and permissions
About this article
Cite this article
Angelov, S., Khanna, S. & Kunal, K. The Network as a Storage Device: Dynamic Routing with Bounded Buffers. Algorithmica 55, 71–94 (2009). https://doi.org/10.1007/s00453-007-9143-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00453-007-9143-1