Advertisement

Towards Flexible Demands in Online Leasing Problems

  • Shouwei Li
  • Alexander Mäcker
  • Christine MarkarianEmail author
  • Friedhelm Meyer auf der Heide
  • Sören Riechers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9198)

Abstract

We consider online leasing problems in which demands arrive over time and need to be served by leasing resources. We introduce a new model for these problems such that a resource can be leased for K different durations each incurring a different cost (longer leases cost less per time unit). Each demand i can be served anytime between its arrival \(a_i\) and its deadline \(a_i + d_i\) by a leased resource. The objective is to meet all deadlines while minimizing the total leasing costs. This model is a natural generalization of Meyerson’s ParkingPermitProblem (FOCS 2005) in which \(d_i=0\) for all i. We propose an online algorithm that is \(\Theta (K + \frac{d_{max}}{l_{min}})\)-competitive where \(d_{max}\) and \(l_{min}\) denote the largest \(d_i\) and the shortest available lease length, respectively. We also extend the SetCoverLeasing problem by deadlines and give a competitive online algorithm which also improves on existing solutions for the original SetCoverLeasing problem.

Keywords

Online algorithms Leasing Infrastructure problems Parking permit problem Deadlines 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Meyerson, A.: The parking permit problem. In: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science(FOCS), pp. 274–284 (2005)Google Scholar
  2. 2.
    Meyerson, A.: Online facility location. In: Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science(FOCS), pp. 426–431 (2001)Google Scholar
  3. 3.
    Alon, N., Awerbuch, B., Azar, Y., Buchbinder, N., Naor, J.: The online set cover problem. In: Proceedings of the 35th Annual ACM Symposium on the Theory of Computation(STOC), pp. 100–105 (2003)Google Scholar
  4. 4.
    Berman, P., Coulston, C.: Online algorithms for Steiner tree problems. In: Proceedings of the 29th Annual ACM Symposium on the Theory of Computation(STOC), pp. 344–353 (1997)Google Scholar
  5. 5.
    Ben-Yehuda, O., Ben-Yehuda, M., Schuster, A., Tsafrir, D.: Deconstructing amazon EC2 spot instance pricing. In: Proceedings of the 3rd IEEE International Conference on Cloud Computing Technology and Science(Cloud-Com), pp. 304–311 (2011)Google Scholar
  6. 6.
    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) Google Scholar
  7. 7.
    Nagarajan, C., Williamson, D.P.: Offline and online facility leasing. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) IPCO 2008. LNCS, vol. 5035, pp. 303–315. Springer, Heidelberg (2008) Google Scholar
  8. 8.
    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) Google Scholar
  9. 9.
    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, Heidelberg (2014) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Shouwei Li
    • 1
  • Alexander Mäcker
    • 1
  • Christine Markarian
    • 1
    Email author
  • Friedhelm Meyer auf der Heide
    • 1
  • Sören Riechers
    • 1
  1. 1.Heinz Nixdorf Institute and Computer Science DepartmentUniversity of PaderbornPaderbornGermany

Personalised recommendations