Abstract
In the contiguous variant of the Scheduling with Interval Conflicts problem, there is a universe \(\mathcal{U}\) consisting of elements being consecutive positive integers. An input is a sequence of conflicts in the form of intervals of length at most σ. For each conflict, an algorithm has to choose at most one surviving element, with the ultimate goal of maximizing the number of elements that survived all conflicts. We present an O(logσ/ loglogσ)-competitive randomized algorithm for this problem, beating known lower bound of Ω(logσ) that holds for deterministic algorithms.
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.
References
Awerbuch, B., Bartal, Y., Fiat, A., Rosén, A.: Competitive non-preemptive call control. In: Proc. of the 5th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 312–320 (1994)
Bachmann, U.T., Halldórsson, M.M., Shachnai, H.: Online selection of intervals and t-intervals. Information and Computation 233, 1–11 (2013); Also appeared in Proc. of the 12th SWAT, pp. 383–394 (2010)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)
Chrobak, M.: Online aggregation problems. SIGACT News 45(1), 91–102 (2014)
Emek, Y., Halldórsson, M.M., Mansour, Y., Patt-Shamir, B., Radhakrishnan, J., Rawitz, D.: Online set packing. SIAM Journal on Computing 41(4), 728–746 (2012); Also appeared as Online set packing and competitive scheduling of multi-part tasks. In: Proc. of the 29th PODC, pp. 440–449 (2010)
Garay, J.A., Gopal, I.S.: Call preemption in communication networks. In: Proc. of the 11th IEEE Int. Conference on Computer Communications (INFOCOM), pp. 1043–1050 (1992)
Garay, J.A., Gopal, I.S., Kutten, S., Mansour, Y., Yung, M.: Efficient on-line call control algorithms. Journal of Algorithms 23(1), 180–194 (1997)
Garefalakis, T.: A new family of randomized algorithms for list accessing. In: Burkard, R.E., Woeginger, G.J. (eds.) ESA 1997. LNCS, vol. 1284, pp. 200–216. Springer, Heidelberg (1997)
Halldórsson, M.M., Patt-Shamir, B., Rawitz, D.: Online scheduling with interval conflicts. Theory of Computing Systems 53(2), 300–317 (2013); Also appeared in Proc. of the 28th STACS, pp. 472–483 (2011)
Irani, S.: Two results on the list update problem. Information Processing Letters 38(6), 301–306 (1991)
Jaromczyk, J.W., Pezarski, A., Ślusarek, M.: An optimal competitive on-line algorithm for the minimal clique cover problem in interval and circular-arc graphs. In: Proc. of the 19th European Workshop on Computational Geometry, EWCG (2003)
Lipton, R.J., Tomkins, A.: Online interval scheduling. In: Proc. of the 5th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 302–311 (1994)
Reingold, N., Westbrook, J., Sleator, D.D.: Randomized competitive algorithms for the list update problem. Algorithmica 11(1), 15–32 (1994)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28(2), 202–208 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Bienkowski, M., Kraska, A., Schmidt, P. (2015). A Randomized Algorithm for Online Scheduling with Interval Conflicts. In: Scheideler, C. (eds) Structural Information and Communication Complexity. SIROCCO 2015. Lecture Notes in Computer Science(), vol 9439. Springer, Cham. https://doi.org/10.1007/978-3-319-25258-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-25258-2_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25257-5
Online ISBN: 978-3-319-25258-2
eBook Packages: Computer ScienceComputer Science (R0)