Abstract
We study the online problem of reading articles that are listed in an aggregated form in a dynamic stream, e.g., in news feeds, as abbreviated social media posts, or in the daily update of new articles on arXiv. In such a context, the brief information on an article in the listing only hints at its content. We consider readers who want to maximize their information gain within a limited time budget, hence either discarding an article right away based on the hint or accessing it for reading. The reader can decide at any point whether to continue with the current article or skip the remaining part irrevocably. In this regard, Reading Articles Online, RAO, does differ substantially from the Online Knapsack Problem, but also has its similarities. Under mild assumptions, we show that any \(\alpha \)-competitive algorithm for the Online Knapsack Problem in the random order model can be used as a black box to obtain an \((\mathrm {e}+ \alpha )C\)-competitive algorithm for RAO, where C measures the accuracy of the hints with respect to the information profiles of the articles. Specifically, with the current best algorithm for Online Knapsack, which is \(6.65<2.45\mathrm {e}\)-competitive, we obtain an upper bound of \(3.45\mathrm {e}C\) on the competitive ratio of RAO. Furthermore, we study a natural algorithm that decides whether or not to read an article based on a single threshold value, which can serve as a model of human readers. We show that this algorithmic technique is O(C)-competitive. Hence, our algorithms are constant-competitive whenever the accuracy C is a constant.
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
Similar content being viewed by others
Notes
- 1.
Disjointness is obtained by random, consistent tie-breaking as described in [4].
- 2.
In [4], it is implicitly assumed that \(\sum _{i\in [n]} t_i\ge 3/2\) as their choice of \(\gamma \) is 3/2.
- 3.
As the hints are distinct by Assumption 1.
- 4.
Note that the Chernoff Bound is indeed applicable since the random variables \(t_iy_{[n]}^{(\beta )}(i)\zeta _i\) and \(t_iy_{[n]}^{(\gamma )}(i)(1-\zeta _i)\) are discrete and \(\zeta _i\) are mutually independent.
References
Agrawal, S., Shadravan, M., Stein, C.: Submodular secretary problem with shortlists. In: Blum, A. (ed.) 10th Innovations in Theoretical Computer Science Conference, ITCS 2019, San Diego, California, USA, LIPIcs, vol. 124, pp. 1:1–1:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
Albers, S., Khan, A., Ladewig, L.: Improved online algorithms for knapsack and GAP in the random order model. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019, Massachusetts Institute of Technology, Cambridge, MA, USA, pp. 22:1–22:23 (2019)
Albers, S., Ladewig, L.: New results for the k-Secretary problem. In: Lu, P., Zhang, G. (eds.) 30th International Symposium on Algorithms and Computation (ISAAC 2019), Leibniz International Proceedings in Informatics (LIPIcs), vol. 149, pp. 18:1–18:19. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl (2019)
Babaioff, M., Immorlica, N., Kempe, D., Kleinberg, R.: A knapsack secretary problem with applications. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) APPROX/RANDOM -2007. LNCS, vol. 4627, pp. 16–28. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74208-1_2
Babaioff, M., Immorlica, N., Kempe, D., Kleinberg, R.: Matroid secretary problems. J. ACM 65(6), 35:1–35:26 (2018)
Dean, B.C., Goemans, M.X., Vondrák, J.: Approximating the stochastic knapsack problem: the benefit of adaptivity. Math. Oper. Res. 33(4), 945–964 (2008)
Dynkin, E.B.: Optimal choice of the stopping moment of a Markov process. Sov. Math. 4, 627–629 (1963)
Freire, M.L.M., Potts, D., Dayama, N.R., Oulasvirta, A., Di Francesco, M.: Foraging-based optimization of pervasive displays. Pervasive Mob. Comput. 55, 45–58 (2019)
Goerigk, M., Gupta, M., Ide, J., Schöbel, A., Sen, S.: The robust knapsack problem with queries. Comput. & OR 55, 12–22 (2015)
Kesselheim, T., Radke, K., Tönnis, A., Vöcking, B.: Primal beats dual on online packing LPs in the random-order model. SIAM J. Comput. 47(5), 1939–1964 (2018)
Kleinberg, R.D.: A multiple-choice secretary algorithm with applications to online auctions. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, Vancouver, British Columbia, Canada, pp. 630–631 (2005)
Marchetti-Spaccamela, A., Vercellis, C.: Stochastic on-line knapsack problems. Math. Program. 68, 73–104 (1995). https://doi.org/10.1007/BF01585758
Maxima: Maxima, a Computer Algebra System. Version 5.43.2 (2019). http://maxima.sourceforge.net/
Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis. Cambridge University Press, Cambridge (2017)
Noga, J., Sarbua, V.: An online partially fractional knapsack problem. In: 8th International Symposium on Parallel Architectures, Algorithms, and Networks, ISPAN 2005, Las Vegas, Nevada, USA, pp. 108–112 (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Karrenbauer, A., Kovalevskaya, E. (2020). Reading Articles Online. In: Wu, W., Zhang, Z. (eds) Combinatorial Optimization and Applications. COCOA 2020. Lecture Notes in Computer Science(), vol 12577. Springer, Cham. https://doi.org/10.1007/978-3-030-64843-5_43
Download citation
DOI: https://doi.org/10.1007/978-3-030-64843-5_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-64842-8
Online ISBN: 978-3-030-64843-5
eBook Packages: Computer ScienceComputer Science (R0)