article

On shortest path representation

Authors:

Gábor Rétvári,

József J. Bíró,

Tibor CinklerAuthors Info & Claims

IEEE/ACM Transactions on Networking (TON), Volume 15, Issue 6

Pages 1293 - 1306

https://doi.org/10.1109/TNET.2007.900708

Published: 01 December 2007 Publication History

Abstract

Lately, it has been proposed to use shortest path first routing to implement Traffic Engineering in IP networks. The idea is to set the link weights so that the shortest paths, and the traffic thereof, follow the paths designated by the operator. Clearly, only certain shortest path representable path sets can be used in this setting, that is, paths which become shortest paths over some appropriately chosen positive, integer-valued link weights. Our main objective in this paper is to distill and unify the theory of shortest path representability under the umbrella of a novel flow-theoretic framework. In the first part of the paper, we introduce our framework and state a descriptive necessary and sufficient condition to characterize shortest path representable paths. Unfortunately, traditional methods to calculate the corresponding link weights usually produce a bunch of superfluous shortest paths, often leading to congestion along the unconsidered paths. Thus, the second part of the paper is devoted to reducing the number of paths in a representation to the bare minimum. To the best of our knowledge, this is the first time that an algorithm is proposed, which is not only able to find a minimal representation in polynomial time, but also assures link weight integrality. Moreover, we give a necessary and sufficient condition to the existence of a one-to-one mapping between a path set and its shortest path representation. However, as revealed by our simulation studies, this condition seems overly restrictive and instead, minimal representations prove much more beneficial

References

[1]

{1} D. Awduchen, A. Chiu, A. Elwalid, I. Widjaja, and X. Xiao, "Overview and Principles of Internet Traffic Engineering," RFC 3272, May 2002.

[2]

{2} Z. Wang, Internet QoS: Architectures and Mechanisms for Quality of Service. San Diego, CA: Academic Press, 2001.

[3]

{3} J. Moy, "OSPF Version 2," RFC 2328, Apr. 1998.

[4]

{4} Intermediate System to Intermediate System Routing Information Exchange Protocol for Use in Conjunction With the Protocol for Providing the Connectionless-Mode Network Service (ISO 8473), ISO/IEC 10589:1992.

[5]

{5} B. Fortz, J. Rexford, and M. Thorup, "Traffic engineering with traditional IP routing protocols," IEEE Commun. Mag., vol. 40, no. 10, pp. 118-124, Oct 2002.

[6]

{6} G. Rétvári, R. Szabó, and J. J. Bíró, "On the representability of arbitrary path sets as shortest paths: Theory, algorithms, and complexity," in Lecture Notes in Computer Science: Proc. 3rd Int. IFIP-TC6 Networking Conf., Athens, Greece, May 2004, pp. 1180-1191.

[7]

{7} B. Fortz and M. Thorup, "Internet traffic engineering by optimizing OSPF weights," in Proc. IEEE INFOCOM, 2000, pp. 519-528.

[8]

{8} B. Fortz and M. Thorup, "Increasing Internet capacity using local search," 2000 {Online}. Available: http://www.research.att.com/ ~mthorup/PAPERS/or_ospf.ps

[9]

{9} M. Pióro, A. Szentesi, J. Harmatos, A. Juttner, P. Gajowniczek, and S. Kozdrowski, "On open shortest path first related network optimisation problems," Perform. Eval., vol. 48, pp. 201-223, May 2002.

[10]

{10} B. Fortz and M. Thorup, "Optimizing OSPF/IS-IS weights in a changing world," IEEE J. Sel. Areas Commun., vol. 20, no. 5, pp. 756-767, May 2002.

[11]

{11} G. Rétvári and T. Cinkler, "Practical OSPF traffic engineering," IEEE Commun. Lett., vol. 8, no. 11, pp. 689-691, Nov 2004.

[12]

{12} A. Farago, B. Szviatovszki, and A. Szentesi, "Inverse optimization in high-speed networks," Discrete Appl. Math., vol. 129, pp. 83-98, Jun. 2003.

[13]

{13} R. K. Ahuja and J. B. Orlin, "Inverse optimization, part I: linear programming and general problem," MIT Loan School of Management, Cambridge, MA, Working paper, 1998.

[14]

{14} J. L. Sobrinho, "Algebra and algorithms for QoS path computation and hop-by-hop routing in the Internet," in Proc. IEEE INFOCOM, 2001, pp. 727-735.

[15]

{15} R. Guerin, A. Orda, and D. Williams, "QoS routing mechanisms and OSPF extensions," IETF RFC 2676, 1999.

[16]

{16} M. Pióro and D. Medhi, Routing, Flow, and Capacity Design in Communication and Computer Networks. San Diego, CA: Morgan Kaufmann, Nov 2004.

[17]

{17} W. Ben-Ameur and E. Gourdin, "Internet routing and related topology issues," SIAM J. Discrete Math., vol. 17, no. 1, pp. 18-49, 2003.

[18]

{18} Z. Wang, Y. Wang, and L. Zhang, "Internet traffic engineering without full-mesh overlaying," in Proc. IEEE INFOCOM, 2001, vol. 1, pp. 565-571.

[19]

{19} A. Sridharan, C. Diot, and R. Guérin, "Achieving near-optimal traffic engineering solutions for current OSPF/IS-IS networks," in Proc. IEEE INFOCOM, 2003, vol. 2, pp. 1167-1177.

[20]

{20} R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications. Englewood Cliffs, NJ: Prentice-Hall, 1993.

[21]

{21} M. S. Bazaraa, J. J. Jarvis, and H. D. Sherali, Linear Programming and Network Flows. New York: Wiley, 1990.

[22]

{22} J. L. Kennington, "A survey of linear cost multicommodity network flows," Oper. Res., vol. 26, no. 2, pp. 209-236, 1978.

[23]

{23} T. Leighton, C. Stein, F. Makedon, É. Tardos, S. Plotkin, and S. Tragoudas, "Fast approximation algorithms for multicommodity flow problems," in Proc. 23rd Annu. ACM Symp. Theory of Computing, May 1991, pp. 101-111.

[24]

{24} G. Rétvári, J. J. Bíró, and T. Cinkler, "A novel Lagrangian relaxation to the minimum cost multicommodity flow problem and its application to OSPF traffic engineering," in Proc. 9th IEEE Symp. Computers and Communications (ISCC'2004), Alexandria, Egypt, Jun. 2004, vol. 2, pp. 957-962.

[25]

{25} G. Rétvári, T. Cinkler, and J. J. Bíró, "Notes on Shortest Path Representation," Tech. Rep. 2005-02, Feb 2005 {Online}. Available: http:// qosip.tmit.bme.hu/~retvari/publications/SPR_tech_rep.pdf

[26]

{26} J. Evans, "The simplex method for integral multicommodity networks," Naval Research Logistics Quarterly, vol. 25, pp. 31-37, Mar 1978.

[27]

{27} A. Medina, A. Lakhina, I. Matta, and J. Byers, "BRITE: Universal Topology Generation From A User's Perspective," Comput. Sci. Dept., Boston Univ., Tech. Rep. 2001-003, 2001, 1.

[28]

{28} Z. Wang and J. Crowcroft, "Quality-of-service routing for supporting multimedia applications," IEEE J. Sel. Areas Commun., vol. 14, no. 7, pp. 1228-1234, Jul. 1996.

Cited By

Shaikh NCastro L(2018)Random Node Pair Sampling-Based Estimation of Average Path Lengths in NetworksInternational Journal of Operations Research and Information Systems10.4018/IJORIS.20180701029:3(27-51)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.4018/IJORIS.2018070102
Nmeth KKrsi ARtvri G(2017)Optimal resource pooling over legacy equal-split load balancing schemesComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2017.08.017127:C(243-265)Online publication date: 9-Nov-2017
https://dl.acm.org/doi/10.1016/j.comnet.2017.08.017
Ma CHe RXiang W(2016)Optimising hazardous materials transport network based on multi-objective hybrid intelligence algorithmInternational Journal of Intelligent Systems Technologies and Applications10.1504/IJISTA.2016.07609815:1(52-62)Online publication date: 1-Apr-2016
https://dl.acm.org/doi/10.1504/IJISTA.2016.076098
Show More Cited By

Recommendations

Inapproximability results for the inverse shortest paths problem with integer lengths and unique shortest paths

We study the complexity of two inverse shortest paths (ISP) problems with integer arc lengths and the requirement for uniquely determined shortest paths. Given a collection of paths in a directed graph D = (V, A), the task is to find positive integer arc ...
On the approximability of the minimum congestion unsplittable shortest path routing problem
IPCO'05: Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization

We are given an undirected simple graph G = (V,E) with edge capacities $c_{e} \epsilon \mathcal{Z}+$, e ∈ E, and a set K⊆V² of commodities with demand values d_(s,t)εℤ, (s, t) ∈ K. An unsplittable shortest path routing (USPR) of the commodities K is a ...
Generalization of Shortest Path Map
ITNG '10: Proceedings of the 2010 Seventh International Conference on Information Technology: New Generations

We consider the problem of constructing shortest path maps in two dimensions under angle constraint. Shortest path maps are used for planning short length paths from a fixed source point s to varying goal points. In the standard shortest path map the ...

Comments

Information & Contributors

Information

Published In

cover image IEEE/ACM Transactions on Networking

IEEE/ACM Transactions on Networking Volume 15, Issue 6

December 2007

400 pages

ISSN:1063-6692

Issue’s Table of Contents

Publisher

IEEE Press

Publication History

Published: 01 December 2007

Published in TON Volume 15, Issue 6

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

7
Total Citations
View Citations
385
Total Downloads

Downloads (Last 12 months)3
Downloads (Last 6 weeks)0

Reflects downloads up to 06 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Shaikh NCastro L(2018)Random Node Pair Sampling-Based Estimation of Average Path Lengths in NetworksInternational Journal of Operations Research and Information Systems10.4018/IJORIS.20180701029:3(27-51)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.4018/IJORIS.2018070102
Nmeth KKrsi ARtvri G(2017)Optimal resource pooling over legacy equal-split load balancing schemesComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2017.08.017127:C(243-265)Online publication date: 9-Nov-2017
https://dl.acm.org/doi/10.1016/j.comnet.2017.08.017
Ma CHe RXiang W(2016)Optimising hazardous materials transport network based on multi-objective hybrid intelligence algorithmInternational Journal of Intelligent Systems Technologies and Applications10.1504/IJISTA.2016.07609815:1(52-62)Online publication date: 1-Apr-2016
https://dl.acm.org/doi/10.1504/IJISTA.2016.076098
Xu KShen MLiu HLiu JLi FLi T(2016)Achieving Optimal Traffic Engineering Using a Generalized Routing FrameworkIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2015.239276027:1(51-65)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1109/TPDS.2015.2392760
Kusetogullari HLeeson MKole BHines E(2014)Meta-heuristic algorithms for optimized network flow wavelet-based image codingApplied Soft Computing10.1016/j.asoc.2013.09.00114(536-553)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1016/j.asoc.2013.09.001
Ortega-Arranz HTorres YGonzalez-Escribano ALlanos D(2014)Optimizing an APSP implementation for NVIDIA GPUs using kernel characterization criteriaThe Journal of Supercomputing10.1007/s11227-014-1212-z70:2(786-798)Online publication date: 1-Nov-2014
https://dl.acm.org/doi/10.1007/s11227-014-1212-z
Rétvári GNémeth FChaparadza RSzabó R(2009)OSPF for Implementing Self-adaptive Routing in Autonomic NetworksProceedings of the 4th IEEE International Workshop on Modelling Autonomic Communications Environments10.1007/978-3-642-05006-0_6(72-85)Online publication date: 22-Oct-2009
https://dl.acm.org/doi/10.1007/978-3-642-05006-0_6

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents