research-article

Public Access

Costly Circuits, Submodular Schedules and Approximate Carathéodory Theorems

Authors:

Shaileshh Bojja Venkatakrishnan,

Mohammad Alizadeh,

Pramod ViswanathAuthors Info & Claims

ACM SIGMETRICS Performance Evaluation Review, Volume 44, Issue 1

Pages 75 - 88

https://doi.org/10.1145/2964791.2901479

Published: 14 June 2016 Publication History

Abstract

Hybrid switching -- in which a high bandwidth circuit switch (optical or wireless) is used in conjunction with a low bandwidth packet switch -- is a promising alternative to interconnect servers in today's large scale data centers. Circuit switches offer a very high link rate, but incur a non-trivial reconfiguration delay which makes their scheduling challenging. In this paper, we demonstrate a lightweight, simple and nearly-optimal scheduling algorithm that trades-off reconfiguration costs with the benefits of reconfiguration that match the traffic demands. Seen alternatively, the algorithm provides a fast and approximate solution towards a constructive version of Caratheodory's Theorem for the Birkhoff polytope. The algorithm also has strong connections to submodular optimization, achieves a performance at least half that of the optimal schedule and strictly outperforms state of the art in a variety of traffic demand settings. These ideas naturally generalize: we see that indirect routing leads to exponential connectivity; this is another phenomenon of the power of multi-hop routing, distinct from the well-known load balancing effects.

References

[1]

R. Ahuja, T. Magnanti, and J. Orlin. Network flows: theory, algorithms, and applications. Prentice Hall, 1993.

Digital Library

[2]

M. Al-Fares, S. Radhakrishnan, B. Raghavan, N. Huang, and A. Vahdat. Hedera: Dynamic flow scheduling for data center networks. In NSDI, volume 10, pages 19--19, 2010.

Digital Library

[3]

M. Alizadeh, A. Greenberg, D. A. Maltz, J. Padhye, P. Patel, B. Prabhakar, S. Sengupta, and M. Sridharan. Data center tcp (dctcp). SIGCOMM, 2011.

Digital Library

[4]

S. Arora, E. Hazan, and S. Kale. The multiplicative weights update method: a meta-algorithm and applications. Theory of Computing, 8(1):121--164, 2012.

[5]

Y. Azar and I. Gamzu. Efficient submodular function maximization under linear packing constraints. In Automata, Languages, and Programming, pages 38--50. Springer, 2012.

Digital Library

[6]

S. Barman. Approximating nash equilibria and dense bipartite subgraphs via an approximate version of caratheodory's theorem. In Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, pages 361--369. ACM, 2015.

Digital Library

[7]

C. Barnhart and Y. Sheffi. A network-based primal-dual heuristic for the solution of multicommodity network flow problems. Transportation Science, 27(2):102--117, 1993.

Digital Library

[8]

T. Benson, A. Akella, and D. A. Maltz. Network traffic characteristics of data centers in the wild. In SIGCOMM, 2010.

Digital Library

[9]

Z. Cao, M. Kodialam, and T. Lakshman. Joint static and dynamic traffic scheduling in data center networks. In INFOCOM, 2014.

[10]

C.-S. Chang, W.-J. Chen, and H.-Y. Huang. Birkhoff-von neumann input buffered crossbar switches. In INFOCOM, 2000.

[11]

C.-S. Chang, D.-S. Lee, and Y.-S. Jou. Load balanced birkhoff-von neumann switches. In High Performance Switching and Routing, 2001 IEEE Workshop on, pages 276--280. IEEE, 2001.

[12]

A. Dasylva and R. Srikant. Optimal wdm schedules for optical star networks. IEEE/ACM Transactions on Networking (TON), 7(3):446--456, 1999.

Digital Library

[13]

R. Duan and S. Pettie. Linear-time approximation for maximum weight matching. J. ACM, 61(1):1:1--1:23, Jan. 2014.

Digital Library

[14]

R. Duan and H.-H. Su. A scaling algorithm for maximum weight matching in bipartite graphs. In SODA, 2012.

Digital Library

[15]

N. Farrington. Optics in data center network architecture. PhD thesis, Citeseer, 2012.

Digital Library

[16]

N. Farrington, G. Porter, S. Radhakrishnan, H. H. Bazzaz, V. Subramanya, Y. Fainman, G. Papen, and A. Vahdat. Helios: a hybrid electrical/optical switch architecture for modular data centers. SIGCOMM, 2011.

Digital Library

[17]

P. F. Felzenszwalb and R. Zabih. Dynamic programming and graph algorithms in computer vision. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 33(4):721--740, 2011.

Digital Library

[18]

M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM (JACM), 34(3):596--615, 1987.

Digital Library

[19]

S. Fu, B. Wu, X. Jiang, A. Pattavina, L. Zhang, and S. Xu. Cost and delay tradeoff in three-stage switch architecture for data center networks. In HPSR, 2013.

[20]

N. Garg and J. Koenemann. Faster and simpler algorithms for multicommodity flow and other fractional packing problems. SIAM Journal on Computing, 37(2):630--652, 2007.

Digital Library

[21]

P. Giaccone, B. Prabhakar, and D. Shah. Randomized scheduling algorithms for high-aggregate bandwidth switches. Selected Areas in Communications, IEEE Journal on, 21(4):546--559, 2003.

Digital Library

[22]

I. S. Gopal and C. K. Wong. Minimizing the number of switchings in an ss/tdma system. Communications, IEEE Transactions on, 33(6):497--501, 1985.

[23]

A. Greenberg, P. Lahiri, D. A. Maltz, P. Patel, and S. Sengupta. Towards a next generation data center architecture: scalability and commoditization. In Proceedings of the ACM workshop on Programmable routers for extensible services of tomorrow, pages 57--62. ACM, 2008.

Digital Library

[24]

M. Grötschel, L. Lovász, and A. Schrijver. Geometric algorithms and combinatorial optimization. Algorithms and combinatorics. Springer-Verlag, 1993.

[25]

N. Hamedazimi, Z. Qazi, H. Gupta, V. Sekar, S. R. Das, J. P. Longtin, H. Shah, and A. Tanwer. Firefly: a reconfigurable wireless data center fabric using free-space optics. In SIGCOMM, 2014.

Digital Library

[26]

T. Inukai. An efficient ss/tdma time slot assignment algorithm. Communications, IEEE Transactions on, 27(10):1449--1455, 1979.

[27]

S. Kandula, J. Padhye, and P. Bahl. Flyways to de-congest data center networks. 2009.

[28]

I. Keslassy, C.-S. Chang, N. McKeown, and D.-S. Lee. Optimal load-balancing. In INFOCOM, 2005.

[29]

I. Keslassy, M. Kodialam, T. Lakshman, and D. Stiliadis. On guaranteed smooth scheduling for input-queued switches. In INFOCOM, 2003.

[30]

T. Leighton, F. Makedon, S. Plotkin, C. Stein, É. Tardos, and S. Tragoudas. Fast approximation algorithms for multicommodity flow problems. Journal of Computer and System Sciences, 50(2):228--243, 1995.

Digital Library

[31]

X. Li and M. Hamdi. On scheduling optical packet switches with reconfiguration delay. Selected Areas in Communications, IEEE Journal on, 21(7):1156--1164, 2003.

Digital Library

[32]

Y. Li, S. Panwar, and H. J. Chao. Frame-based matching algorithms for optical switches. In High Performance Switching and Routing, 2003, HPSR. Workshop on, pages 97--102. IEEE, 2003.

[33]

H. Liu, F. Lu, A. Forencich, R. Kapoor, M. Tewari, G. M. Voelker, G. Papen, A. C. Snoeren, and G. Porter. Circuit switching under the radar with reactor. In NSDI, 2014.

Digital Library

[34]

H. Liu, M. K. Mukerjee, C. Li, N. Feltman, G. Papen, S. Savage, S. Seshan, G. M. Voelker, D. G. Andersen, M. Kaminsky, G. Porter, and A. C. Snoeren. Scheduling techniques for hybrid circuit/packet networks. In ACM CoNEXT, 2015.

Digital Library

[35]

N. McKeown. The islip scheduling algorithm for input-queued switches. Networking, IEEE/ACM Transactions on, 7(2):188--201, 1999.

Digital Library

[36]

N. McKeown, A. Mekkittikul, V. Anantharam, and J. Walrand. Achieving 100% throughput in an input-queued switch. Communications, IEEE Transactions on, 47(8):1260--1267, 1999.

[37]

A. Mekkittikul and N. McKeown. A practical scheduling algorithm to achieve 100% throughput in input-queued switches. In INFOCOM, 1998.

Digital Library

[38]

V. Mirrokni, R. P. Leme, A. Vladu, and S. C.-w. Wong. Tight bounds for approximate carathéodory and beyond. arXiv preprint arXiv:1512.08602, 2015.

[39]

S. Pettie and P. Sanders. A simpler linear time 2/3- $\varepsilon$ approximation for maximum weight matching. Information Processing Letters, 91(6):271--276, 2004.

Digital Library

[40]

G. Porter, R. Strong, N. Farrington, A. Forencich, P. Chen-Sun, T. Rosing, Y. Fainman, G. Papen, and A. Vahdat. Integrating microsecond circuit switching into the data center. SIGCOMM, 2013.

Digital Library

[41]

B. Prabhakar and N. McKeown. On the speedup required for combined input-and output-queued switching. Automatica, 35(12):1909--1920, 1999.

Digital Library

[42]

M. O. Rabin. Efficient dispersal of information for security, load balancing, and fault tolerance. Journal of the ACM (JACM), 36(2):335--348, 1989.

Digital Library

[43]

A. Roy, H. Zeng, J. Bagga, G. Porter, and A. C. Snoeren. Inside the social network's (datacenter) network. In SIGCOMM, 2015.

Digital Library

[44]

A. Schrijver. Combinatorial Optimization - Polyhedra and Efficiency. Springer, 2003.

[45]

A. Shieh, S. Kandula, A. G. Greenberg, and C. Kim. Seawall: Performance isolation for cloud datacenter networks. In HotCloud, 2010.

Digital Library

[46]

A. Singla, A. Singh, and Y. Chen. Osa: An optical switching architecture for data center networks with unprecedented flexibility. In NSDI, 2012.

Digital Library

[47]

R. Srikant and L. Ying. Communication Networks: An Optimization, Control and Stochastic Networks Perspective. Cambridge University Press, New York, NY, USA, 2014.

Digital Library

[48]

B. Towles and W. J. Dally. Guaranteed scheduling for switches with configuration overhead. Networking, IEEE/ACM Transactions on, 11(5):835--847, 2003.

Digital Library

[49]

L. G. Valiant. A bridging model for parallel computation. Communications of the ACM, 33(8):103--111, 1990.

Digital Library

[50]

S. B. Venkatakrishnan, M. Alizadeh, and P. Viswanath. Costly circuits, submodular schedules: Hybrid switch scheduling for data centers. CoRR, abs/1512.01271, 2015.

[51]

C.-H. Wang and T. Javidi. Adaptive policies for scheduling with reconfiguration delay: An end-to-end solution for all-optical data centers. arXiv preprint arXiv:1511.03417, 2015.

[52]

C.-H. Wang, T. Javidi, and G. Porter. End-to-end scheduling for all-optical data centers. In Computer Communications (INFOCOM), 2015 IEEE Conference on, pages 406--414. IEEE, 2015.

[53]

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. Ng, M. Kozuch, and M. Ryan. c-through: Part-time optics in data centers. SIGCOMM, 2011.

Digital Library

[54]

B. Wu and K. L. Yeung. Nxg05--6: Minimum delay scheduling in scalable hybrid electronic/optical packet switches. In GLOBECOM, 2006.

[55]

B. Wu, K. L. Yeung, and X. Wang. Nxg06--4: Improving scheduling efficiency for high-speed routers with optical switch fabrics. In GLOBECOM, 2006.

[56]

X. Zhou, Z. Zhang, Y. Zhu, Y. Li, S. Kumar, A. Vahdat, B. Y. Zhao, and H. Zheng. Mirror mirror on the ceiling: Flexible wireless links for data centers. SIGCOMM, 2012.

Digital Library

Cited By

Zhang SShao JChen BSun WHu W(2024)Interruptible Scheduling of Partially Re-Configurable Optical Switching in Data Center NetworksJournal of Lightwave Technology10.1109/JLT.2023.334104242:7(2212-2224)Online publication date: 1-Apr-2024
https://doi.org/10.1109/JLT.2023.3341042
Han SLee EYoo HNamseok KPack S(2024)P4ToR: Conflict-Free Distributed Scheduling for Hybrid Optical/Electrical Datacenter NetworksIEEE INFOCOM 2024 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)10.1109/INFOCOMWKSHPS61880.2024.10620800(1-2)Online publication date: 20-May-2024
https://doi.org/10.1109/INFOCOMWKSHPS61880.2024.10620800
Dai WDinitz MFoerster KLuo LSchmid S(2024)Approximation Algorithms for Minimizing Congestion in Demand-Aware NetworksIEEE INFOCOM 2024 - IEEE Conference on Computer Communications10.1109/INFOCOM52122.2024.10621340(1461-1470)Online publication date: 20-May-2024
https://doi.org/10.1109/INFOCOM52122.2024.10621340
Show More Cited By

Index Terms

Costly Circuits, Submodular Schedules and Approximate Carathéodory Theorems
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Approximation algorithms
      2. Network flows
  2. Mathematical analysis
    1. Mathematical optimization
      1. Mixed discrete-continuous optimization
        Submodular optimization and polymatroids
2. Networks

Recommendations

Costly Circuits, Submodular Schedules and Approximate Carathéodory Theorems
SIGMETRICS '16: Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science

Hybrid switching -- in which a high bandwidth circuit switch (optical or wireless) is used in conjunction with a low bandwidth packet switch -- is a promising alternative to interconnect servers in today's large scale data centers. Circuit switches ...
Costly circuits, submodular schedules and approximate Carathéodory Theorems

Hybrid switching--in which a high bandwidth circuit switch (optical or wireless) is used in conjunction with a low bandwidth packet switch--is a promising alternative to interconnect servers in today's large-scale data centers. Circuit switches offer a ...
Carathéodory-type Theorems à la Bárány

We generalise the famous Helly---Lovász theorem leading to a generalisation of the Bárány---Carathéodory theorem for oriented matroids in dimension ≤3. We also provide a non-metric proof of the latter colourful theorem for arbitrary dimensions and ...

Comments

Information & Contributors

Information

Published In

cover image ACM SIGMETRICS Performance Evaluation Review

ACM SIGMETRICS Performance Evaluation Review Volume 44, Issue 1

Performance evaluation review

June 2016

409 pages

ISSN:0163-5999

DOI:10.1145/2964791

Editors:
Derek Eager
University of Saskatchewan
,
Carey Williamson
University of Calgary

Issue’s Table of Contents

SIGMETRICS '16: Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science
June 2016
434 pages
ISBN:9781450342667
DOI:10.1145/2896377
General Chairs:
Sara Alouf
Inria, France
,
Alain Jean-Marie
Inria, France
,
Program Chairs:
Nidhi Hegde
Bell Labs, France
,
Alexandre Proutière
KTH, Sweden

Copyright © 2016 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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 June 2016

Published in SIGMETRICS Volume 44, Issue 1

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

37
Total Citations
View Citations
908
Total Downloads

Downloads (Last 12 months)201
Downloads (Last 6 weeks)27

Reflects downloads up to 17 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Zhang SShao JChen BSun WHu W(2024)Interruptible Scheduling of Partially Re-Configurable Optical Switching in Data Center NetworksJournal of Lightwave Technology10.1109/JLT.2023.334104242:7(2212-2224)Online publication date: 1-Apr-2024
https://doi.org/10.1109/JLT.2023.3341042
Han SLee EYoo HNamseok KPack S(2024)P4ToR: Conflict-Free Distributed Scheduling for Hybrid Optical/Electrical Datacenter NetworksIEEE INFOCOM 2024 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)10.1109/INFOCOMWKSHPS61880.2024.10620800(1-2)Online publication date: 20-May-2024
https://doi.org/10.1109/INFOCOMWKSHPS61880.2024.10620800
Dai WDinitz MFoerster KLuo LSchmid S(2024)Approximation Algorithms for Minimizing Congestion in Demand-Aware NetworksIEEE INFOCOM 2024 - IEEE Conference on Computer Communications10.1109/INFOCOM52122.2024.10621340(1461-1470)Online publication date: 20-May-2024
https://doi.org/10.1109/INFOCOM52122.2024.10621340
Reisacher MFrank RBlenk A(2023)FactoryDC: Network and Resource Planning for Emerging Applications in Future FactoriesProceedings of the 1st Workshop on Enhanced Network Techniques and Technologies for the Industrial IoT to Cloud Continuum10.1145/3609389.3610564(1-7)Online publication date: 10-Sep-2023
https://dl.acm.org/doi/10.1145/3609389.3610564
Teh MZhao SCao PBergman K(2023)Enabling Quasi-Static Reconfigurable Networks With Robust Topology EngineeringIEEE/ACM Transactions on Networking10.1109/TNET.2022.321053431:3(1056-1070)Online publication date: Jun-2023
https://doi.org/10.1109/TNET.2022.3210534
Zerwas JPoese ISchmid SBlenk A(2022)On the Benefits of Joint Optimization of Reconfigurable CDN-ISP InfrastructureIEEE Transactions on Network and Service Management10.1109/TNSM.2021.311913419:1(158-173)Online publication date: Mar-2022
https://doi.org/10.1109/TNSM.2021.3119134
Ye TLi JPan XLee T(2022)Asynchronous Optical Traffic Offloading of Hybrid Optical/Electrical Data Center NetworksIEEE Transactions on Cloud Computing10.1109/TCC.2020.299248910:2(805-820)Online publication date: 1-Apr-2022
https://doi.org/10.1109/TCC.2020.2992489
Hall MFoerster KSchmid SDurairajan R(2021)A Survey of Reconfigurable Optical NetworksOptical Switching and Networking10.1016/j.osn.2021.100621(100621)Online publication date: Mar-2021
https://doi.org/10.1016/j.osn.2021.100621
Foerster KSchmid S(2019)Survey of Reconfigurable Data Center NetworksACM SIGACT News10.1145/3351452.335146450:2(62-79)Online publication date: 24-Jul-2019
https://dl.acm.org/doi/10.1145/3351452.3351464
Liu LXu JSingh MJohnson KSpillner JKlusáček DAnjum A(2019)LESSProceedings of the 12th IEEE/ACM International Conference on Utility and Cloud Computing10.1145/3344341.3368807(187-197)Online publication date: 2-Dec-2019
https://dl.acm.org/doi/10.1145/3344341.3368807
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

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 Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents