Skip to main content
SpringerLink
Log in

Hardness of Routing for Minimizing Superlinear Polynomial Cost in Directed Graphs

  • Conference paper
  • First Online:
Theory and Applications of Models of Computation (TAMC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10185))

  • 826 Accesses

Abstract

We study the problem of routing in directed graphs with superlinear polynomial costs, which is significant for improving the energy efficiency of networks. In this problem, we are given a directed graph G(V, E) and a set of traffic demands. Routing \(\delta _{e}\) units of demands along an edge e will incur a cost of \(f_{e}(\delta _{e}) = \mu _{e} (\delta _{e})^{\alpha }\) with \(\mu _{e} > 0\) and \(\alpha >1\). The objective is to find integral routing paths for minimizing \(\sum _{e}f_{e}(\delta _{e})\). Through developing a new labeling technique and applying it to a randomized reduction, we prove an \(\varOmega \Big ( {\big ( \frac{\log |E|}{ \log \log |E|} \big )^{\alpha }} \cdot |E|^{-\frac{1}{4}} \Big )\)-hardness factor for this problem under the assumption that \(NP\nsubseteq \text {ZPTIME}(n^{\hbox {polylog}(n)})\).

This work is supported by the National Natural Science Foundation of China (NSFC) Major International Collaboration Project 61520106005 and NSFC Project for Innovation Groups 61521092.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Andrews, M., Antonakopoulos, S., Zhang, L.: Minimum-cost network design with (dis)economies of scale. In: 2010 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), FOCS 2010, pp. 585–592, October 2010

    Google Scholar 

  2. Andrews, M., Chuzhoy, J., Guruswami, V., Khanna, S., Talwar, K., Zhang, L.: Inapproximability of edge-disjoint paths and low congestion routing on undirected graphs. Combinatorica 30(5), 485–520 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Andrews, M., Fernandez Anta, A., Zhang, L., Zhao, W.: Routing for power minimization in the speed scaling model. IEEE/ACM Trans. Networking 20(1), 285–294 (2012)

    Article  Google Scholar 

  4. Andrews, M., Zhang, L.: Hardness of the undirected congestion minimization problem. In: Proceedings of the Thirty-seventh Annual ACM Symposium on Theory of Computing, STOC 2005, pp. 284–293. ACM (2005)

    Google Scholar 

  5. Andrews, M., Zhang, L.: Logarithmic hardness of the directed congestion minimization problem. In: Proceedings of the Thirty-eighth Annual ACM Symposium on Theory of Computing, STOC 2006, pp. 517–526. ACM (2006)

    Google Scholar 

  6. Bampis, E., Kononov, A., Letsios, D., Lucarelli, G., Sviridenko, M.: Energy efficient scheduling and routing via randomized rounding. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2013, Guwahati, India, 12–14 December 2013, pp. 449–460 (2013)

    Google Scholar 

  7. Bansal, N., Gupta, A., Krishnaswamy, R., Nagarajan, V., Pruhs, K., Stein, C.: Multicast routing for energy minimization using speed scaling. In: Even, G., Rawitz, D. (eds.) MedAlg 2012. LNCS, vol. 7659, pp. 37–51. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34862-4_3

    Chapter  Google Scholar 

  8. Chuzhoy, J., Guruswami, V., Khanna, S., Talwar, K.: Hardness of routing with congestion in directed graphs. In: Proceedings of the Thirty-ninth Annual ACM Symposium on Theory of Computing, STOC 2007, pp. 165–178. ACM (2007)

    Google Scholar 

  9. Dobiński, G.: Summirung der reihe \(\sum n^m / n!\), für m= 1, 2, 3, 4, 5. Arch. für Mat. und Physik 61, 333–336 (1877)

    MATH  Google Scholar 

  10. Fettweis, G., Zimmermann, E.: ICT energy consumption-trends and challenges. In: Proceedings of the 11th International Symposium on Wireless Personal Multimedia Communications, vol. 2, p. 6 (2008)

    Google Scholar 

  11. Gupta, A., Krishnaswamy, R., Pruhs, K.: Online primal-dual for non-linear optimization with applications to speed scaling. In: Erlebach, T., Persiano, G. (eds.) WAOA 2012. LNCS, vol. 7846, pp. 173–186. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38016-7_15

    Chapter  Google Scholar 

  12. Kaxiras, S., Martonosi, M.: Computer Architecture Techniques for Power-Efficiency, 1st edn. Morgan and Claypool Publishers (2008)

    Google Scholar 

  13. Makarychev, K., Sviridenko, M.: Solving optimization problems with diseconomies of scale via decoupling. In: 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS), pp. 571–580, October 2014

    Google Scholar 

  14. Shi, Y., Zhang, F., Wu, J., Liu, Z.: Randomized oblivious integral routing for minimizing power cost. Theor. Comput. Sci. 607(Part 2), 221–246 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wierman, A., Andrew, L., Tang, A.: Power-aware speed scaling in processor sharing systems. In: INFOCOM 2009, pp. 2007–2015. IEEE, April 2009

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computing Technology, Chinese Academy of Sciences (ICT, CAS), Beijing, China

    Yangguang Shi, Fa Zhang & Zhiyong Liu

  2. University of Chinese Academy of Sciences, Beijing, China

    Yangguang Shi

  3. Key Laboratory of Intelligent Information Processing, ICT, CAS, Beijing, China

    Fa Zhang

  4. Beijing Key Laboratory of Mobile Computing and Pervasive Device, ICT, CAS, Beijing, China

    Yangguang Shi & Zhiyong Liu

Authors
  1. Yangguang Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fa Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiyong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiyong Liu .

Editor information

Editors and Affiliations

  1. Anna University, Chennai, India

    T.V. Gopal

  2. Universität Bern , Bern, Switzerland

    Gerhard Jäger

  3. Universität Bern , Bern, Switzerland

    Silvia Steila

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Shi, Y., Zhang, F., Liu, Z. (2017). Hardness of Routing for Minimizing Superlinear Polynomial Cost in Directed Graphs. In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-55911-7_41

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55910-0

  • Online ISBN: 978-3-319-55911-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation