article

Oblivious routing on node-capacitated and directed graphs

Authors:

Mohammad Taghi Hajiaghayi,

Robert D. Kleinberg,

Tom LeightonAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 3, Issue 4

Pages 51 - es

https://doi.org/10.1145/1290672.1290688

Published: 01 November 2007 Publication History

Abstract

Oblivious routing algorithms for general undirected networks were introduced by Räcke [2002], and this work has led to many subsequent improvements and applications. Comparatively little is known about oblivious routing in general directed networks, or even in undirected networks with node capacities.

We present the first nontrivial upper bounds for both these cases, providing algorithms for k-commodity oblivious routing problems with competitive ratio O(√k log(n)) for undirected node-capacitated graphs and O(√k n^1/4 log(n)) for directed graphs. In the special case that all commodities have a common source or sink, our upper bound becomes O(√n log(n)) in both cases, matching the lower bound up to a factor of log(n). The lower bound (which first appeared in Azar et al. [2003]) is obtained on a graph with very high degree. We show that, in fact, the degree of a graph is a crucial parameter for node-capacitated oblivious routing in undirected graphs, by providing an O(Δ polylog(n))-competitive oblivious routing scheme for graphs of degree Δ. For the directed case, however, we show that the lower bound of Ω(√n) still holds in low-degree graphs.

Finally, we settle an open question about routing problems in which all commodities share a common source or sink. We show that even in this simplified scenario there are networks in which no oblivious routing algorithm can achieve a competitive ratio better than Ω(log n).

References

[1]

Alon, N., Awerbuch, B., Azar, Y., Buchbinder, N., and Naor, J. S. 2004. A general approach to online network optimization problems. In Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA), 577--586.

Digital Library

[2]

Aspnes, J., Azar, Y., Fiat, A., Plotkin, S. A., and Waarts, O. 1997. On-Line routing of virtual circuits with applications to load balancing and machine scheduling. J. ACM 44, 3, 486--504. Also in Proceedings of the 25th STOC, 1993, 623--631.

Digital Library

[3]

Awerbuch, B., and Azar, Y. 1994. Local optimization of global objectives: Competitive distributed deadlock resolution and resource allocation. In Proceedings of the 35th IEEE Symposium on Foundations of Computer Science (FOCS), 240--249.

[4]

Awerbuch, B., and Leighton, F. T. 1993. A simple local-control approximation algorithm for multicommodity flow. In Proceedings of the 34th IEEE Symposium on Foundations of Computer Science (FOCS), 459--468.

[5]

Awerbuch, B., and Leighton, F. T. 1994. Improved approximation algorithms for the multi-commodity flow problem and local competitive routing in dynamic networks. In Proceedings of the 26th ACM Symposium on Theory of Computing (STOC), 487--496.

Digital Library

[6]

Azar, Y., Cohen, E., Fiat, A., Kaplan, H., and Räcke, H. 2003. Optimal oblivious routing in polynomial time. In Proceedings of the 35th ACM Symposium on Theory of Computing (STOC), 383--388.

Digital Library

[7]

Bartal, Y., and Leonardi, S. 1999. On-Line routing in all-optical networks. Theor. Comput. Sci. 221, 1-2, 19--39. Also in Proceedings of the 24th ICALP, 1997, 516--526.

Digital Library

[8]

Bienkowski, M., Korzeniowski, M., and Räcke, H. 2003. A practical algorithm for constructing oblivious routing schemes. In Proceedings of the 15th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 24--33.

Digital Library

[9]

Chekuri, C., Khanna, S., and Shepherd, B. 2004. The all-or-nothing multicommodity flow problem. In Proceedings of the 36th ACM Symposium on Theory of Computing (STOC), 156--165.

Digital Library

[10]

Even, G., Naor, J. S., Schieber, B., and Sudan, M. 1998. Approximating minimum feedback sets and multicuts in directed graphs. Algorithmica 20, 2, 151--174.

[11]

Garg, N., Vazirani, V. V., and Yannakakis, M. 1996. Approximate max-flow min-(multi)cut theorems and their applications. SIAM J. Comput. 25, 2, 235--251.

Digital Library

[12]

Garg, N., Vazirani, V. V., and Yannakakis, M. 2004. Multiway cuts in node weighted graphs. J. Algorithms 50, 1, 49--61.

Digital Library

[13]

Hajiaghayi, M. T., and Räcke, H. An O(&sqrt;n)-approximation algorithm for directed sparsest cut. Inf. Proc. Lett. to appear.

Digital Library

[14]

Harrelson, C., Hildrum, K., and Rao, S. B. 2003. A polynomial-time tree decomposition to minimize congestion. In Proceedings of the 15th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 34--43.

Digital Library

[15]

Klein, P. N., Plotkin, S. A., Rao, S. B., and Tardos, É. 1997. Approximation algorithms for Steiner and directed multicuts. J. Alg. 22, 2, 241--269.

Digital Library

[16]

Maggs, B. M., Meyer auf der Heide, F., Vöcking, B., and Westermann, M. 1997. Exploiting locality for networks of limited bandwidth. In Proceedings of the 38th IEEE Symposium on Foundations of Computer Science (FOCS), 284--293.

Digital Library

[17]

Maggs, B. M., Miller, G. L., Parekh, O., Ravi, R., and Woo, S. L. M. 2005. Finding effective support-tree preconditioners. In Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 176--185.

Digital Library

[18]

Räcke, H. 2002. Minimizing congestion in general networks. In Proceedings of the 43rd IEEE Symposium on Foundations of Computer Science (FOCS), 43--52.

Digital Library

[19]

Valiant, L., G., and Brebner, G. J. 1981. Universal schemes for parallel communication. In Proceedings of the 13th ACM Symposium on Theory of Computing (STOC), 263--277.

Digital Library

Cited By

Bernstein AGutenberg MSaranurak T(2022)Deterministic Decremental SSSP and Approximate Min-Cost Flow in Almost-Linear Time2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00100(1000-1008)Online publication date: Feb-2022
https://doi.org/10.1109/FOCS52979.2021.00100
Al-Najjar YBen-Ameur WLeguay J(2021)On the approximability of robust network designTheoretical Computer Science10.1016/j.tcs.2021.01.026860(41-50)Online publication date: Mar-2021
https://doi.org/10.1016/j.tcs.2021.01.026
P. Kamal Devi (2020)Identification of shortest path with Dijkstra’s algorithm through the distribution function analysis of flow and connectivity in non-directed graphsMalaya Journal of Matematik10.26637/MJM0804/01808:04(2346-2351)Online publication date: 1-Oct-2020
https://doi.org/10.26637/MJM0804/0180
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Index Terms

Oblivious routing on node-capacitated and directed graphs
1. Networks
  1. Network protocols
    1. Network layer protocols
      1. Routing protocols
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 3, Issue 4

November 2007

293 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1290672

Issue’s Table of Contents

Copyright © 2007 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 November 2007

Published in TALG Volume 3, Issue 4

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Cited By

Bernstein AGutenberg MSaranurak T(2022)Deterministic Decremental SSSP and Approximate Min-Cost Flow in Almost-Linear Time2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00100(1000-1008)Online publication date: Feb-2022
https://doi.org/10.1109/FOCS52979.2021.00100
Al-Najjar YBen-Ameur WLeguay J(2021)On the approximability of robust network designTheoretical Computer Science10.1016/j.tcs.2021.01.026860(41-50)Online publication date: Mar-2021
https://doi.org/10.1016/j.tcs.2021.01.026
P. Kamal Devi (2020)Identification of shortest path with Dijkstra’s algorithm through the distribution function analysis of flow and connectivity in non-directed graphsMalaya Journal of Matematik10.26637/MJM0804/01808:04(2346-2351)Online publication date: 1-Oct-2020
https://doi.org/10.26637/MJM0804/0180
Guo LPang JWalid A(2018)Joint Placement and Routing of Network Function Chains in Data CentersIEEE INFOCOM 2018 - IEEE Conference on Computer Communications10.1109/INFOCOM.2018.8486429(612-620)Online publication date: Apr-2018
https://doi.org/10.1109/INFOCOM.2018.8486429
Christodoulou GSgouritsa AKlein P(2017)An improved upper bound for the universal TSP on the gridProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039750(1006-1021)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039750
Ene AMiller GPachocki JSidford AWichs DMansour Y(2016)Routing under balanceProceedings of the forty-eighth annual ACM symposium on Theory of Computing10.1145/2897518.2897654(598-611)Online publication date: 19-Jun-2016
https://dl.acm.org/doi/10.1145/2897518.2897654
Boroojeni KAmini MIyengar S(2016)An Oblivious Routing-Based Power Flow Calculation Method for Loss Minimization of Smart Power Networks: A Theoretical Perspective2016 15th IEEE International Conference on Machine Learning and Applications (ICMLA)10.1109/ICMLA.2016.0113(641-645)Online publication date: Dec-2016
https://doi.org/10.1109/ICMLA.2016.0113
Censor-Hillel KGhaffari MKuhn FHalldórsson MDolev S(2014)Distributed connectivity decompositionProceedings of the 2014 ACM symposium on Principles of distributed computing10.1145/2611462.2611491(156-165)Online publication date: 15-Jul-2014
https://dl.acm.org/doi/10.1145/2611462.2611491
Goyal NOlver NBruce Shepherd F(2011)Dynamic vs. Oblivious Routing in Network DesignAlgorithmica10.5555/2616915.261694061:1(161-173)Online publication date: 1-Sep-2011
https://dl.acm.org/doi/10.5555/2616915.2616940
Thiam FDeMarco C(2010)Optimal transmission expansion via intrinsic properties of power flow conditioningNorth American Power Symposium 201010.1109/NAPS.2010.5618969(1-8)Online publication date: Sep-2010
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