Abstract
A t-interval is a union of at most t half-open intervals on the real line. An interval is the special case where t = 1. Requests for contiguous allocation of a linear resource can be modeled as a sequence of t-intervals. We consider the problems of online selection of intervals and t-intervals, which show up in Video-on-Demand services, high speed networks and molecular biology, among others. We derive lower bounds and (almost) matching upper bounds on the competitive ratios of randomized algorithms for selecting intervals, 2-intervals and t-intervals, for any t > 2. While offline t-interval selection has been studied before, the online version is considered here for the first time.
Supported by Icelandic Research Fund (grant 060034022).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Awerbuch, B., Bartal, Y., Fiat, A., Rosén, A.: Competitive non-preemptive call control. In: SODA, pp. 312–320 (1994)
Bachmann, U.T.: Online t-Interval Scheduling. MSc thesis, School of CS, Reykjavik Univ. (December 2009)
Bachmann, U.T., Halldórsson, M.M., Shachnai, H.: Online selection of intervals and t-intervals (2010), http://www.cs.technion.ac.il/~hadas/PUB/onint_full.pdf
Bar-Yehuda, R., Halldórsson, M.M., Naor, J.S., Shachnai, H., Shapira, I.: Scheduling split intervals. In: SODA, pp. 732–741 (2002)
Bar-Yehuda, R., Rawitz, D.: Using fractional primal-dual to schedule split intervals with demands. Discrete Optimization 3(4), 275–287 (2006)
Butman, A., Hermelin, D., Lewenstein, M., Rawitz, D.: Optimization problems in multiple-interval graphs. In: SODA (2007)
Halldórsson, M.M., Iwama, K., Miyazaki, S., Taketomi, S.: Online independent sets. Theoretical Computer Science 289(2), 953–962 (2002)
Halldórsson, M.M., Szegedy, M.: Lower bounds for on-line graph coloring. Theoretical Comput. Sci. 130, 163–174 (1994)
Kierstead, H.A., Trotter, W.T.: An extremal problem in recursive combinatorics. In: Congr. Numer., vol. 33, pp. 143–153 (1981)
Kleinberg, J., Tardos, E.: Algorithm Design. Addison-Wesley, Reading (2005)
Kolen, A.W., Lenstra, J.K., Papadimitriou, C.H., Spieksma, F.C.: Interval scheduling: A survey. Naval Research Logistics 54, 530–543 (2007)
Lipton, R.J., Tomkins, A.: Online interval scheduling. In: SODA, pp. 302–311 (1994)
Spieksma, F.: On the approximability of an interval scheduling problem. J. Sched. 2, 215–227 (1999)
Woeginger, G.J.: On-line scheduling of jobs with fixed start and end times. Theor. Comput. Sci. 130(1), 5–16 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bachmann, U.T., Halldórsson, M.M., Shachnai, H. (2010). Online Selection of Intervals and t-Intervals. In: Kaplan, H. (eds) Algorithm Theory - SWAT 2010. SWAT 2010. Lecture Notes in Computer Science, vol 6139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13731-0_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-13731-0_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13730-3
Online ISBN: 978-3-642-13731-0
eBook Packages: Computer ScienceComputer Science (R0)