Skip to main content

Metrical Service Systems with Multiple Servers

  • Conference paper
Computing and Combinatorics (COCOON 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7936))

Included in the following conference series:

Abstract

The problem of metrical service systems with multiple servers ((k,l)-MSSMS) proposed by Feuerstein [16] is to service requests, each of which is an l-point subset of a metric space, using k servers in an online manner, minimizing the distance traveled by the servers. We prove that Feuerstein’s deterministic algorithm actually achieves an improved competitive ratio of \(k\left({{k+l}\choose{l}}-1\right)\) on uniform metrics. In the randomized online setting on uniform metrics, we give an algorithm which achieves a competitive ratio \(\mathcal{O}(k^3\log l)\), beating the deterministic lower bound of \({{k+l}\choose{l}}-1\). We prove that any randomized algorithm for MSSMS on uniform metrics must be Ω(logkl)-competitive. On arbitrary metric spaces, we have deterministic lower bounds which are significantly larger than the bound for uniform metrics [8].

For the offline (k,l)-MSSMS, we give a factor l pseudo-approximation algorithm using kl servers on any metric space, and prove a matching hardness result, that a pseudo-approximation using less than kl servers is unlikely, even on uniform metrics.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bansal, N., Buchbinder, N., Madry, A., Naor, J.: A polylogarithmic-competitive algorithm for the k-server problem. In: IEEE 52nd Annual Symposium on Foundations of Computer Science, pp. 267–276. IEEE (2011)

    Google Scholar 

  2. Bansal, N., Buchbinder, N., Naor, J.: A primal-dual randomized algorithm for weighted paging. In: 48th Annual IEEE Symposium on Foundations of Computer Science, pp. 507–517. IEEE Computer Society (2007)

    Google Scholar 

  3. Bartal, Y., Bollobás, B., Mendel, M.: A ramsey-type theorem for metric spaces and its applications for metrical task systems and related problems. In: 42nd Annual Symposium on Foundations of Computer Science, pp. 396–405. IEEE Computer Society (2001)

    Google Scholar 

  4. Bartal, Y., Grove, E.: The harmonic k-server algorithm is competitive. Journal of the ACM 47(1), 1–15 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press (1998)

    Google Scholar 

  6. Borodin, A., El-Yaniv, R.: On randomization in on-line computation. Information and Computation 150(2), 244–267 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Burley, W.R.: Traversing layered graphs using the work function algorithm. Journal of Algorithms 20(3), 479–511 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chiplunkar, A., Vishwanathan, S.: Metrical service systems with multiple servers. CoRR, abs/1206.5392 (2012)

    Google Scholar 

  9. Chrobak, M., Karloff, H.J., Payne, T.H., Vishwanathan, S.: New results on server problems. SIAM Journal on Discrete Mathematics 4(2), 172–181 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chrobak, M., Larmore, L.L.: The server problem and on-line games. In: On-Line Algorithms: Proceedings of a DIMACS Workshop. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 7, pp. 11–64 (1992)

    Google Scholar 

  11. Chrobak, M., Larmore, L.L.: An optimal on-line algorithm for k-servers on trees. SIAM Journal on Computing 20(1), 144–148 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chrobak, M., Larmore, L.L.: Metrical service systems: Deterministic strategies. Technical report (1993)

    Google Scholar 

  13. Chrobak, M., Sgall, J.: The weighted 2-server problem. Theoretical Computer Science 324(2-3), 289–312 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dinur, I., Guruswami, V., Khot, S., Regev, O.: A new multilayered PCP and the hardness of hypergraph vertex cover. SIAM Journal on Computing 34(5), 1129–1146 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Dinur, I., Safra, S.: The importance of being biased. In: Proceedings on 34th Annual ACM Symposium on Theory of Computing, pp. 33–42. ACM (2002)

    Google Scholar 

  16. Feuerstein, E.: Uniform Service Systems with k Servers. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, pp. 23–32. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  17. Fiat, A., Foster, D.P., Karloff, H.J., Rabani, Y., Ravid, Y., Vishwanathan, S.: Competitive algorithms for layered graph traversal. SIAM Journal on Computing 28(2), 447–462 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fiat, A., Rabani, Y., Ravid, Y.: Competitive k-server algorithms (extended abstract). In: 31st Annual Symposium on Foundations of Computer Science, pp. 454–463. IEEE Computer Society (1990)

    Google Scholar 

  19. Fiat, A., Ricklin, M.: Competitive algorithms for the weighted server problem. Theoretical Computer Science 130(1), 85–99 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  20. Grove, E.F.: The harmonic online k-server algorithm is competitive. In: Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pp. 260–266. ACM (1991)

    Google Scholar 

  21. Karlin, A.R., Manasse, M.S., McGeoch, L.A., Owicki, S.S.: Competitive randomized algorithms for nonuniform problems. Algorithmica 11(6), 542–571 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  22. Khot, S.: On the power of unique 2-prover 1-round games. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pp. 767–775. ACM (2002)

    Google Scholar 

  23. Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2 − ε. Journal of Computer and System Sciences 74(3), 335–349 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  24. Koutsoupias, E.: The k-server problem. Computer Science Review 3(2), 105–118 (2009)

    Article  Google Scholar 

  25. Koutsoupias, E., Papadimitriou, C.H.: On the k-server conjecture. Journal of the ACM 42(5), 971–983 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  26. Lovász, L.: Flats in matroids and geometric graphs. In: Proc. Sixth British Combinatorial Conf., Combinatorial Surveys, Royal Holloway Coll., Egham, pp. 45–86. Academic Press, London (1977)

    Google Scholar 

  27. Manasse, M.S., McGeoch, L.A., Sleator, D.D.: Competitive algorithms for on-line problems. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, pp. 322–333. ACM (1988)

    Google Scholar 

  28. Papadimitriou, C.H., Yannakakis, M.: Shortest paths without a map. Theoretical Computer Science 84(1), 127–150 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ramesh, H.: On traversing layered graphs on-line. Journal of Algorithms 18(3), 480–512 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  30. Sitters, R.: The generalized work function algorithm is competitive for the generalized 2-server problem. CoRR, abs/1110.6600 (2011)

    Google Scholar 

  31. Stougie, L., Vestjens, A.P.A.: Randomized algorithms for on-line scheduling problems: how low can’t you go? Operations Research Letters 30(2), 89–96 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  32. Yao, A.C.-C.: Probabilistic computations: Toward a unified measure of complexity (extended abstract). In: 18th Annual Symposium on Foundations of Computer Science, pp. 222–227. IEEE Computer Society (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chiplunkar, A., Vishwanathan, S. (2013). Metrical Service Systems with Multiple Servers. In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38768-5_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38767-8

  • Online ISBN: 978-3-642-38768-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics