Price Fluctuation in Online Leasing

  • Björn Feldkord
  • Christine Markarian
  • Friedhelm Meyer Auf der Heide
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10628)

Abstract

Current theoretical attempts towards understanding real-life leasing scenarios assume the following leasing model. Demands arrive with time and need to be served by leased resources. Different types of leases are available, each with a fixed duration and price, respecting economy of scale (longer leases cost less per unit time). An online algorithm is to serve each arriving demand while minimizing the total leasing costs and without knowing future demands. In this paper, we generalize this model into one in which lease prices fluctuate with time and are not known to the algorithm in advance. Hence, an online algorithm is to perform under the uncertainty of both demands and lease prices. We consider different adversarial models and provide online algorithms, evaluated using standard competitive analysis. For each of these models, we give deterministic matching upper and lower bounds.

Keywords

Online algorithms Leasing Infrastructure problems Parking permit problem Ski-rental problem 

References

  1. 1.
    Abshoff, S., Kling, P., Markarian, C., Meyer auf der Heide, F., Pietrzyk, P.: Towards the price of leasing online. J. Comb. Optim., 1–20 (2015)Google Scholar
  2. 2.
    Abshoff, S., Markarian, C., Meyer auf der Heide, F.: Randomized online algorithms for set cover leasing problems. In: Zhang, Z., Wu, L., Xu, W., Du, D.-Z. (eds.) COCOA 2014. LNCS, vol. 8881, pp. 25–34. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12691-3_3 Google Scholar
  3. 3.
    Andrews, M., Zhang, L.: Wavelength assignment in optical networks with fixed fiber capacity. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 134–145. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27836-8_14 CrossRefGoogle Scholar
  4. 4.
    Anthony, B.M., Gupta, A.: Infrastructure leasing problems. In: Fischetti, M., Williamson, D.P. (eds.) IPCO 2007. LNCS, vol. 4513, pp. 424–438. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72792-7_32 CrossRefGoogle Scholar
  5. 5.
    Bienkowski, M.: Price fluctuations: to buy or to rent. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 25–36. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12450-1_3 CrossRefGoogle Scholar
  6. 6.
    Bienkowski, M., Kraska, A., Schmidt, P.: A deterministic algorithm for online steiner tree leasing. Algorithms and Data Structures. LNCS, vol. 10389, pp. 169–180. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62127-2_15 CrossRefGoogle Scholar
  7. 7.
    Hu, X., Ludwig, A., Richa, A., Schmid, S.: Competitive strategies for online cloud resource allocation with discounts: the 2-dimensional parking permit problem. In: 35th IEEE International Conference on Distributed Computing Systems, ICDCS 2015, pp. 93–102. Columbus, OH, USA, 29 June–2 July 2015Google Scholar
  8. 8.
    Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3, 77–119 (1988)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Karp, R.M.: Online algorithms versus offline algorithms: how much is it worth to know the future? In: Algorithms, Software, Architecture - Information Processing 1992, Proceedings of the IFIP 12th World Computer Congress, vol. 1, pp. 416–429. Madrid, Spain, 7–11 September 1992Google Scholar
  10. 10.
    Kling, P., Meyer auf der Heide, F., Pietrzyk, P.: An algorithm for online facility leasing. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 61–72. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31104-8_6 CrossRefGoogle Scholar
  11. 11.
    Li, S., Mäcker, A., Markarian, C., Meyer auf der Heide, F., Riechers, S.: Towards flexible demands in online leasing problems. In: Xu, D., Du, D., Du, D. (eds.) COCOON 2015. LNCS, vol. 9198, pp. 277–288. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21398-9_22 CrossRefGoogle Scholar
  12. 12.
    Markarian, C., Meyer auf der Heide, F.: Online resource leasing. In: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, pp. 343–344. Donostia-San Sebastián, Spain, 21–23 July 2015Google Scholar
  13. 13.
    Meyerson, P.: The parking permit problem. In: Proceedings of 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005), pp. 274–284. Pittsburgh, PA, USA, 23–25 October 2005Google Scholar
  14. 14.
    Nagarajan, C., Williamson, D.P.: Offline and online facility leasing. Discrete Optim. 10(4), 361–370 (2013)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Björn Feldkord
    • 1
  • Christine Markarian
    • 1
  • Friedhelm Meyer Auf der Heide
    • 1
  1. 1.Computer Science Department, Heinz Nixdorf InstitutePaderborn UniversityPaderbornGermany

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