Abstract
In a paper of Borodin, Nielsen and Rackoff [8], a framework for abstracting the properties of deterministic greedy-like algorithms was proposed. We extend their model so as to formally define ”randomized greedy-like algorithms” and be able to prove lower bounds on the approximability of a certain problem by such a class of algorithms. We show how our techniques can be applied in well-studied problems such as the facility location and makespan scheduling problems, for which both upper and lower bounds on the approximation ratio achieved by deterministic greedy-like algorithms are known.
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References
Albers, S.: On randomized online scheduling. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computation, pp. 134–143 (2002)
Angelopoulos, S., Borodin, A.: On the power of priority algorithms for facility location and set cover. In: Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, pp. 26–39 (2002)
Bar-Noy, A., Guha, S., Naor, J., Schieber, B.: Approximating throughput in real-time scheduling. SIAM Journal of Computing 31(2), 331–352 (2001)
Bartal, Y., Fiat, A., Karloff, H., Vohra, R.: New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences 51(3), 359–366 (1995)
Ben-David, S., Borodin, A., Karp, R., Tardos, G., Wigderson, A.: On the power of randomization in online algorithms. Algorithmica 11(1), 2–14 (1994)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Borodin, A., Linial, N., Saks, M.E.: An optimal algorithm for metrical task systems. Journal of the ACM 39(4), 745–763 (1992)
Borodin, A., Nielsen, M., Rackoff, C.: (Incremental) priority algorithms. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 752–761 (2002)
Chen, B., van Vliet, A., Woeginger, G.J.: A lower bound for randomized on-line scheduling algorithms. Information Processing Letters 51, 219–222 (1994)
Chrobak, M., Larmore, L., Reingold, N., Westbrook, J.: A better lower bound on the competitive ratio of the randomized 2-server problem. Information Processing Letters 63, 79–83 (1997)
Fleischer, R., Wahl, M.: Online scheduling revisited. In: Proceedings of the 8th Annual European Symposium on Algorithms, pp. 202–210 (2000)
Fotakis, D.: On the competitive ratio for online facility location. In: Proceedings of the 30th International Colloquium on Automata, Languages and Programming, pp. 637–652 (2003)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, 2nd edn. Freeman, New York (1983)
Gormley, T., Reingold, N., Torng, E., Westbrook, J.: Generating adversaries for request-answer games. In: Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms, pp. 564–565 (2000)
Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Sys. Tech. J. 45, 1563–1581 (1966)
Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM Journal of Applied Mathematics 17(2), 416–429 (1969)
Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. In: Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, pp. 649–657 (1998)
Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: Theoretical and practical results. Journal of the ACM 34(1), 144–162 (1987)
Impagliazzo, R., Davis, S.: Models of greedy algorithms for graph problems. In: Proceedings of the 15th Symposium on Discrete Algorithms (2004) (to appear)
Jain, K., Mahdian, M., Saberi, A.: A new greedy approach for facility location problems. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computation, pp. 731–740 (2002)
Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: A greedy facility location algorithm analyzed using dual fitting. In: Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, pp. 127–137 (2001)
Mahdian, M., Ye, J., Zhang, J.: A 1.52-approximation algorithm for the uncapacitated facility location problem. In: Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, pp. 229–242 (2002)
Mettu, R.R., Plaxton, C.G.: The online median problem. In: Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pp. 339–348 (2000)
Meyerson, A.: Online facility location. In: Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, pp. 426–431 (2001)
Sahni, S.K.: Algorithms for scheduling independent tasks. Journal of the ACM 23(1), 116–127 (1976)
Seiden, S., Sgall, J., Woeginger, G.J.: Semi-online scheduling with decreasing job sizes. Operations Research Letters 27(5), 215–221 (2000)
Sgall, J.: A lower bound for randomized on-line multiprocessor scheduling. Information Processing Letters 63, 51–55 (1997)
Sgall, J.: On-line scheduling–a survey. In: Fiat, A., Woeginger, G. (eds.) Online Algorithms. LNCS, vol. 1442, pp. 196–231. Springer, Heidelberg (1998)
Shmoys, D.B.: Approximation algorithms for facility location problems. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 27–32. Springer, Heidelberg (2000)
Shmoys, D.B., Tardos, E., Aardal, K.: Approximation algorithms for facility location problems (extended abstract). In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 265–274 (1997)
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Angelopoulos, S. (2004). Randomized Priority Algorithms. In: Solis-Oba, R., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2003. Lecture Notes in Computer Science, vol 2909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24592-6_3
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DOI: https://doi.org/10.1007/978-3-540-24592-6_3
Publisher Name: Springer, Berlin, Heidelberg
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