Advertisement

Tight Approximability of the Server Allocation Problem for Real-Time Applications

  • Takehiro Ito
  • Naonori KakimuraEmail author
  • Naoyuki Kamiyama
  • Yusuke Kobayashi
  • Yoshio Okamoto
  • Taichi Shiitada
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10739)

Abstract

The server allocation problem is a facility location problem for a distributed processing scheme on a real-time network. In this problem, we are given a set of users and a set of servers. Then, we consider the following communication process between users and servers. First a user sends his/her request to the nearest server. After receiving all the requests from users, the servers share the requests. A user will then receive the data processed from the nearest server. The goal of this problem is to choose a subset of servers so that the total delay of the above process is minimized. In this paper, we prove the following approximability and inapproximability results. We first show that the server allocation problem has no polynomial-time approximation algorithm unless P = NP. However, assuming that the delays satisfy the triangle inequality, we design a polynomial-time \({3 \over 2}\)-approximation algorithm. When we assume the triangle inequality only among servers, we propose a polynomial-time 2-approximation algorithm. Both of the algorithms are tight in the sense that we cannot obtain better polynomial-time approximation algorithms unless P = NP. Furthermore, we evaluate the practical performance of our algorithms through computational experiments, and show that our algorithms scale better and produce comparable solutions than the previously proposed method based on integer linear programming.

Notes

Acknowledgments

We thank Eiji Oki for bringing the problem into our attention.

References

  1. 1.
    Alumur, S., Kara, B.Y.: Network hub location problems: the state of the art. Eur. J. Oper. Res. 190(1), 1–21 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ba, S., Kawabata, A., Chatterjee, B.C., Oki, E.: Computational time complexity of allocation problem for distributed servers in real-time applications. In: Proceedings of 18th Asia-Pacific Network Operations and Management Symposium, pp. 1–4 (2016)Google Scholar
  3. 3.
    Byrka, J., Pensyl, T., Rybicki, B., Srinivasan, A., Trinh, K.: An improved approximation for \(k\)-median, and positive correlation in budgeted optimization. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 737–756 (2015)Google Scholar
  4. 4.
    Campbell, J.F.: Integer programming formulations of discrete hub location problems. Eur. J. Oper. Res. 72(2), 387–405 (1994)CrossRefzbMATHGoogle Scholar
  5. 5.
    Chen, L.-H., Cheng, D.-W., Hsieh, S.-Y., Hung, L.-J., Lee, C.-W., Wu, B.Y.: Approximation algorithms for single allocation \(k\)-hub center problem. In: Proceedings of the 33rd Workshop on Combinatorial Mathematics and Computation Theory (CMCT 2016), pp. 13–18 (2016)Google Scholar
  6. 6.
    Farahani, R.Z., Hekmatfar, M., Arabani, A.B., Nikbakhsh, E.: Hub location problems: a review of models, classification, solution techniques, and applications. Comput. Ind. Eng. 64(4), 1096–1109 (2013)CrossRefGoogle Scholar
  7. 7.
    Gonzalez, T.F.: Clustering to minimize the maximum intercluster distance. Theor. Comput. Sci. 38, 293–306 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hochbaum, D.S., Shmoys, D.B.: A best possible heuristic for the \(k\)-center problem. Math. Oper. Res. 10(2), 180–184 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Impagliazzo, R., Paturi, R.: On the complexity of \(k\)-SAT. J. Comput. Syst. Sci. 62(2), 367–375 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? J. Comput. Syst. Sci. 63(4), 512–530 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kawabata, A., Chatterjee, B.C., Oki, E.: Distributed processing communication scheme for real-time applications considering admissible delay. In: Proceedings of 2016 IEEE International Workshop Technical Committee on Communications Quality and Reliability, pp. 1–6 (2016)Google Scholar
  12. 12.
    O’Kelly, M.E., Miller, H.J.: Solution strategies for the single facility minimax hub location problem. Pap. Reg. Sci. 70(4), 367–380 (1991)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Takehiro Ito
    • 1
  • Naonori Kakimura
    • 2
    Email author
  • Naoyuki Kamiyama
    • 3
  • Yusuke Kobayashi
    • 4
  • Yoshio Okamoto
    • 5
  • Taichi Shiitada
    • 5
  1. 1.Tohoku UniversitySendaiJapan
  2. 2.Keio UniversityYokohamaJapan
  3. 3.Kyushu UniversityFukuokaJapan
  4. 4.University of TsukubaTsukubaJapan
  5. 5.University of Electro-CommunicationsChofuJapan

Personalised recommendations