Abstract
We consider online competitive algorithms for the problem of collecting weighted items from a dynamic queue S. The content of S varies over time. An update to S can occur between any two consecutive time steps, and it consists in deleting any number of items at the front of S and inserting other items into arbitrary locations in S. At each time step we are allowed to collect one item in S. The objective is to maximize the total weight of collected items. This is a generalization of bounded-delay packet scheduling (also known as buffer management). We present several upper and lower bounds on the competitive ratio for the general case and for some restricted variants of this problem.
References
Andelman, N., Mansour, Y., Zhu, A.: Competitive queueing policies in QoS switches. In: Proceedings of the 14th Symposium on Discrete Algorithms (SODA), pp. 761–770. ACM/SIAM, New York (2003)
Birnbaum, B., Mathieu, C.: On-line bipartite matching made simple. SIGACT News 39(1), 80–87 (2008)
Chin, F.Y.L., Chrobak, M., Fung, S.P.Y., Jawor, W., Sgall, J., Tichý, T.: Online competitive algorithms for maximizing weighted throughput of unit jobs. J. Discrete Algorithms 4, 255–276 (2006)
Chin, F.Y.L., Fung, S.P.Y.: Online scheduling for partial job values: Does timesharing or randomization help? Algorithmica 37, 149–164 (2003)
Englert, M., Westermann, M.: Considering suppressed packets improves buffer management in QoS switches. In: Proceedings of the 18th Symposium on Discrete Algorithms (SODA), pp. 209–218. ACM/SIAM, New York (2007)
Hajek, B.: On the competitiveness of online scheduling of unit-length packets with hard deadlines in slotted time. In: Conference on Information Sciences and Systems, pp. 434–438 (2001)
Jeż, Ł.: One to rule them all: A general randomized algorithm for buffer management with bounded delay. In: Proceedings of the 19th Annual European Symposium on Algorithms (ESA), pp. 239–250 (2011)
Kalyanasundaram, B., Pruhs, K.: An optimal deterministic algorithm for online b-matching. Theor. Comput. Sci. 233(1–2), 319–325 (2000)
Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviridenko, M.: Buffer overflow management in QoS switches. SIAM J. Comput. 33, 563–583 (2004)
Kesselman, A., Mansour, Y., van Stee, R.: Improved competitive guarantees for QoS buffering. Algorithmica 43, 63–80 (2005)
Li, F., Sethuraman, J., Stein, C.: An optimal online algorithm for packet scheduling with agreeable deadlines. In: Proceedings of the 16th Symposium on Discrete Algorithms (SODA), pp. 801–802. ACM/SIAM, New York (2005)
Li, F., Sethuraman, J., Stein, C.: Better online buffer management. In: Proceedings of the 18th Symposium on Discrete Algorithms (SODA), pp. 199–208. ACM/SIAM, New York (2007)
Mehta, A., Saberi, A., Vazirani, U.V., Vazirani, V.V.: Adwords and generalized online matching. J. ACM 54(5), 22 (2007)
Meteor burst communications. http://en.wikipedia.org/wiki/Meteor_burst
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Supported by MNiSW grants N N206 368839, 2010–2013 and N N206 490638, 2010–2011, NSF grants OISE-0340752 and CCF-0729071, and ANR Alpage.
Most of the work was carried out when M. Hurand was at LIX Ecole Polytechnique.
A preliminary version of this paper appeared in the Proceedings of the 20th ACM-SIAM Symposium on Discrete Algorithms (SODA’09).
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Bienkowski, M., Chrobak, M., Dürr, C. et al. Collecting Weighted Items from a Dynamic Queue. Algorithmica 65, 60–94 (2013). https://doi.org/10.1007/s00453-011-9574-6
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DOI: https://doi.org/10.1007/s00453-011-9574-6
Keywords
- Online algorithms
- Competitive analysis
- Packet scheduling
- Buffer management