Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
article

Routing and network design with robustness to changing or uncertain traffic demands

Published: 01 September 2007 Publication History

Abstract

A new class of network design problems were introduced by Fingerhut et al. [26], and independently by Duffield et al. [20], to address, among other things, the issue of uncertainty in the demand matrix. The so-called hose model (the term was coined in [20]) for demand matrices from [26, 20] was subsequently generalized to the polyhedral model by Ben-Ameur and Kerivin [11, 10]. In a different direction, Räacke [51] showed the existence of good randomized oblivious routings in all undirected graphs. This was followed by a proof of the polynomial time solvability of an optimal oblivious routing scheme [7].
One can view the above developments in a common framework of robust optimization. We give a survey of these developments and related work with the aim of providing a unified picture. We also highlight the remaining open problems.

References

[1]
R. Ahuja, T. Magnanti and J. Orlin. Network Flows: Theory, Algorithms and Applications. Prentice Hall, 1993.
[2]
N. Alon, B. Awerbuch, Y. Azar, N. Buchbinder, and J. Naor. A general approach to online network optimization problems. ACM Transactions on Algorithms, 2(4):640--660, 2006.
[3]
A. Altin, E. Amaldi, P. Belotti and M. C. Pinar. Provisioning Virtual Private Networks under Traffic Uncertainty. Networks, 49(1):100--115, 2007. Preliminary version in Proc. of INOC, 250--257, 2005.
[4]
M. Andrews. Hardness of buy-at-bulk network design. Proc. of IEEE FOCS, 115--124, 2004.
[5]
D. Applegate and E. Cohen. Making Intra-Domain Routing Robust to Changing and Uncertain Traffic Demands: Understanding Fundamental Tradeoffs. Proc. of SIGCOMM, 2003.
[6]
S. Arora, S. Rao and U. Vazirani. Expander Flows, Geometric Embeddings and Graph Partitioning. Proc. of ACM STOC, 2004.
[7]
Y. Azar, E. Cohen, A. Fiat, H. Kaplan, and H. Räcke. Optimal oblivious routing in polynomial time. J. of Computer System Sciences (JCSS), 69(3):383--394, 2004. Preliminary version in Proc. of ACM STOC, 2003.
[8]
Y. Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. Proc. of IEEE FOCS, 184--193, 1996.
[9]
Y. Bartal and S. Leonardi. On-line routing in all optical networks. Theor. Comp. Sci., Vol 221, 19--39, 1999.
[10]
W. Ben-Ameur and H. Kerivin. Routing of Uncertain Demands. Optimization and Engineering, 3:283--313, 2005.
[11]
W. Ben-Ameur and H. Kerivin. New economical virtual private networks. Communications of the ACM, Vol 46, 69--73, June 2003.
[12]
M. Bienkowski, M. Korzeniowski, and H. Räcke. A Practical Algorithm for Constructing Oblivious Routing Schemes. Proc. of SPAA, 2003.
[13]
M. Charikar, C. Chekuri, A. Goel, S. Guha, and S. Plotkin. Approximating a Finite Metric by a Small Number of Tree Metrics. Proc. of IEEE FOCS, 1998.
[14]
C. Chekuri, M. Hajiaghayi, G. Kortsarz, and M. Salavatipour. Approximation Algorithms for Non-uniform Buy-at-Bulk Network Design Problems. Proc. of IEEE FOCS, 2006.
[15]
C. Chekuri, M. Hajiaghayi, G. Kortsarz, and M. Salavatipour. Approximation Algorithms for Node-Weighted Buy-at-Bulk Network Design. Proc. of ACM-SIAM SODA, 2007.
[16]
C. Chekuri, S. Khanna, and F. B. Shepherd. The All-or-Nothing Multicommodity Flow Problem. Proc. of ACM STOC, 2004.
[17]
C. Chekuri, S. Khanna, and F. B. Shepherd. Multicommodity Flows, Well-Linked Terminals and Routing Problems. Proc. of ACM STOC, 2005.
[18]
C. Chekuri, G. Oriolo, M. G. Scutella and F. B. Shepherd. Hardness of Robust Network Design. Networks, 50(1):50--54, 2007. Preliminary version appeared in Proc. of INOC, 2005.
[19]
Y. Dodis and S. Khanna. Design Networks with Bounded Pairwise Distance. Proc. of ACM STOC, 750--759, 1999.
[20]
N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe. A Flexible Model for Resource Management in Virtual Private Networks. Proc. of SIGCOMM, 1999.
[21]
F. Eisenbrand and F. Grandoni. An improved approximation algorithm for virtual private network design. In Proc. of ACM-SIAM SODA, 928--932, 2005.
[22]
F. Eisenbrand, F. Grandoni, G. Oriolo and M. Skutella. New Approaches for Virtual Private Network Design. SIAM J. on Computing, 2007. Preliminary version in Proc. of ICALP, LNCS, 1151--1162, 2005.
[23]
F. Grandoni, V. Kaibel, G. Oriolo and M. Skutella. Unpublished manuscript, 2005.
[24]
T. Erlebach and M. Ruegg. Optimal Bandwidth Reservation in Hose-Model VPNs with Multi-Path Routing. Proc. of INFOCOM, March 2004.
[25]
J. Fakcharoenphol, S. Rao, and K. Talwar. A tight bound on approximating arbitrary metrics by tree metrics. JCSS, 69:485--497, 2004. Preliminary version in Proc. of ACM STOC, 2003.
[26]
J. Andrew Fingerhut, S. Suri and J. Turner. Designing Least-Cost Nonblocking Broadband Networks. Journal of Algorithms, 24(2):287--309, 1997.
[27]
M. R. Garey, D. S. Johnson, and L. Stockmeyer Some simplified NP-complete graph problems. Theoretical Computer Science, 1(3):237--267, 1976.
[28]
D. Golovin, V. Nagarajan and M. Singh. Approximating the k-Multicut Problem. Proc. of ACM-SIAM SODA, 621--630, 2006.
[29]
M. Grotschel, L. Lovasz, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization. Springer, 1988.
[30]
S. Guha, A. Meyerson and K. Munagala. Hierarchical Placement and Network Design Problems. Proc. of IEEE FOCS, 2000.
[31]
A. Gupta. Personal communication, 2004.
[32]
A. Gupta, A. Kumar, T. Roughgarden. Simpler and better approximation algorithms for network design. Proc. of ACM STOC, 365--372, 2003.
[33]
A. Gupta, J. Kleinberg, A. Kumar, R. Rastogi, and B. Yener. Provisioning a Virtual Private Network: A Network Design problem for Multicommodity flows. Proc. of ACM STOC, 389--398, 2001.
[34]
A. Gupta, M. Hajiaghayi and H. Räcke. Oblivious Network Design. Proc. of ACM-SIAM SODA, 970--979, 2006.
[35]
M. Hajiaghayi, R. Kleinberg, T. Leighton and H. Raecke. Oblivious Routing on Node-Capacitated and Directed Graphs. Proc. ACM-SIAM SODA, 782--790, 2005.
[36]
M. Hajiahgayi, J. Kim, T. Leighton and H. Raecke. Oblivious routing in directed graphs with random demands. Proc. of ACM STOC, 193--201, 2005.
[37]
C. Harrelson, K. Hildrum, and S. Rao. A polynomial-time tree decomposition to minimize congestion. Proc. of SPAA, 2003.
[38]
C. Hurkens, J. Keijsper, and L. Stougie. Virtual private network design: A proof of the tree routing conjecture on ring networks. SIAM J. on Disc. Math., 2007. Preliminary version in Proc. of IPCO XI, 2005.
[39]
G. Italiano, S. Leonardi and G. Oriolo. Design of Trees in the Hose Model: the Balanced Case. OR Letters, 34(6):601--606, 2006. A preliminary version appeared in Proc. of ARACNE, 65--76, 2002.
[40]
D. Karger and M. Minkoff. Building Steiner Trees with Incomplete Global Knowledge. Proc. of IEEE FOCS, 2000.
[41]
S. Khot. On the power of unique 2-prover 1-round games. Proc. of ACM STOC, 767--775, 2002.
[42]
M. Kodialam, T. Lakshman and S. Sengupta. Efficient and Robust Routing of Highly Variable Traffic. HotNets III, 2004.
[43]
M. Kodialam, T. Lakshman and S. Sengupta. Maximum Throughput Routing of Traffic in the Hose Model Proc. of IEEE INFOCOM, 2006.
[44]
T. Leighton and S. Rao. Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. JACM, 46(6):787--832, 1999. Preliminary version appeared in Proc. of IEEE FOCS, 1988.
[45]
C. Lemaréchal, A. Ouorou and G. Petrou. Robust network design in telecommunications. Proc. of INOC, 258--264, 2005.
[46]
B. Maggs, F. Meyer auf der Heide, B. Vöcking, M. Westerman. Exploiting locality for networks of limited bandwidth. Proc. of IEEE FOCS, 284--293, 1997.
[47]
B. Maggs, G. Miller, O. Parekh, R. Ravi and S. Woo. Finding effective support-tree preconditioners. Proc. of ACM SPAA, 176--185, 2005.
[48]
H. Nagesh, V. Poosala, S. Sengupta, M. Alicherry and V. Kumar. NetSwitch: Load-balanced Data-over-Optical Architecture for Mesh Networks. Lucent Technical Memorandum ITD-04-45867F, 2004.
[49]
H. Nagesh, V. Poosala, V. Kumar, P. Winzer and M. Zirngibl. Load balanced architecture for dynamic traffic. Optical Fiber Communication Conf. (OFC), 2005.
[50]
F. B. Shepherd and P. Winzer. Selective Randomized Load Balancing and Mesh Networks with Changing Demands. Journal of Optical Networking, 5(5):320--339, 2006.
[51]
H. Räcke. Minimizing Congestion in General Networks. Proc. of IEEE FOCS, 43--52, 2002.
[52]
R. Ravi and F. Salman. Approximation Algorithms for the Traveling Purchaser Problem and its Variants in Network Design. Proc. of ESA, 29--40, 1999.
[53]
A. Schrijver. Combinatorial optimization: Polyhedra and efficiency. Springer, 2003.
[54]
L. Valiant. A scheme for fast parallel communication. SIAM J. on Computing, 11(2):350--361, 1982.
[55]
L. Valiant and G. Brebner. Universal schemes for parallel communication. Proc. of ACM STOC, 263--277, 1981.
[56]
R. Zhang-Shen and N. McKeown. Designing a Predictable Internet Backbone Network. HotNets III, San Diego, 2004.

Cited By

View all
  • (2023)Universal Algorithms for Clustering ProblemsACM Transactions on Algorithms10.1145/357284019:2(1-46)Online publication date: 9-Mar-2023
  • (2021)On the Implications of Routing Models on Network OptimizationIEEE Transactions on Network and Service Management10.1109/TNSM.2021.309031218:4(4756-4769)Online publication date: Dec-2021
  • (2021)On the approximability of robust network designTheoretical Computer Science10.1016/j.tcs.2021.01.026860(41-50)Online publication date: Mar-2021
  • Show More Cited By

Index Terms

  1. Routing and network design with robustness to changing or uncertain traffic demands

          Recommendations

          Comments

          Information & Contributors

          Information

          Published In

          cover image ACM SIGACT News
          ACM SIGACT News  Volume 38, Issue 3
          September 2007
          143 pages
          ISSN:0163-5700
          DOI:10.1145/1324215
          Issue’s Table of Contents

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          Published: 01 September 2007
          Published in SIGACT Volume 38, Issue 3

          Check for updates

          Qualifiers

          • Article

          Contributors

          Other Metrics

          Bibliometrics & Citations

          Bibliometrics

          Article Metrics

          • Downloads (Last 12 months)13
          • Downloads (Last 6 weeks)2
          Reflects downloads up to 22 Sep 2024

          Other Metrics

          Citations

          Cited By

          View all
          • (2023)Universal Algorithms for Clustering ProblemsACM Transactions on Algorithms10.1145/357284019:2(1-46)Online publication date: 9-Mar-2023
          • (2021)On the Implications of Routing Models on Network OptimizationIEEE Transactions on Network and Service Management10.1109/TNSM.2021.309031218:4(4756-4769)Online publication date: Dec-2021
          • (2021)On the approximability of robust network designTheoretical Computer Science10.1016/j.tcs.2021.01.026860(41-50)Online publication date: Mar-2021
          • (2021)Affine routing for robust network designNetworks10.1002/net.2207079:4(557-579)Online publication date: 20-Jun-2021
          • (2018)Traffic Engineering with Precomputed PathbooksIEEE INFOCOM 2018 - IEEE Conference on Computer Communications10.1109/INFOCOM.2018.8486419(234-242)Online publication date: Apr-2018
          • (2018) Solving the bifurcated and nonbifurcated robust network loading problem with k ‐adaptive routing Networks10.1002/net.2180772:1(151-170)Online publication date: 6-Feb-2018
          • (2016)Measuring and understanding throughput of network topologiesProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.5555/3014904.3014991(1-12)Online publication date: 13-Nov-2016
          • (2016)Measuring and Understanding Throughput of Network TopologiesSC16: International Conference for High Performance Computing, Networking, Storage and Analysis10.1109/SC.2016.64(761-772)Online publication date: Nov-2016
          • (2015)Energy Conservation Routing in Multihop Wireless NetworksIEEE Transactions on Vehicular Technology10.1109/TVT.2014.235703464:8(3633-3644)Online publication date: Aug-2015
          • (2015)MultiObjective robust network design under uncertain traffic an approach based on evolutionary algorithm2015 Latin American Computing Conference (CLEI)10.1109/CLEI.2015.7359980(1-10)Online publication date: Oct-2015
          • Show More Cited By

          View Options

          Get Access

          Login options

          View options

          PDF

          View or Download as a PDF file.

          PDF

          eReader

          View online with eReader.

          eReader

          Media

          Figures

          Other

          Tables

          Share

          Share

          Share this Publication link

          Share on social media