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Online-bounded analysis

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Abstract

Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance measures, in particular targeted at what seems to be the core problem with competitive analysis: The comparison of the performance of an online algorithm is made with respect to a too powerful adversary. We consider a new approach to restricting the power of the adversary, by requiring that when judging a given online algorithm, the optimal offline algorithm must perform at least as well as the online algorithm, not just on the entire final request sequence, but also on any prefix of that sequence. This is limiting the adversary’s usual advantage of being able to exploit that it knows the sequence is continuing beyond the current request. Through a collection of online problems, including machine scheduling, bin packing, dual bin packing, and seat reservation, we investigate the significance of this particular offline advantage.

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References

  • Albers, S. (1997). On the influence of lookahead in competitive paging algorithms. Algorithmica, 18, 283–305.

    Article  Google Scholar 

  • Albers, S., Favrholdt, L. M., & Giel, O. (2005). On paging with locality of reference. Journal of Computer and System Sciences, 70(2), 145–175.

    Article  Google Scholar 

  • Angelopoulos, S., Dorrigiv, R., & López-Ortiz, A. (2007). On the separation and equivalence of paging strategies. In 18th ACM–SIAM symposium on discrete algorithms (SODA) (pp. 229–237)

  • Azar, Y., Boyar, J., Epstein, L., Favrholdt, L. M., Larsen, K. S., & Nielsen, M. N. (2002). Fair versus unrestricted bin packing. Algorithmica, 34(2), 181–196.

    Article  Google Scholar 

  • Azar, Y., & Epstein, L. (1998). On-line machine covering. Journal of Scheduling, 1(2), 67–77.

    Article  Google Scholar 

  • Azar, Y., & Regev, O. (2001). On-line bin-stretching. Theoretical Computer Science, 268(1), 17–41.

    Article  Google Scholar 

  • Bach, E., Boyar, J., Epstein, L., Favrholdt, L. M., Jiang, T., Larsen, K. S., et al. (2003). Tight bounds on the competitive ratio on accommodating sequences for the seat reservation problem. Journal of Scheduling, 6(2), 131–147.

    Article  Google Scholar 

  • Bansal, N., & Sviridenko, M. (2006). The Santa Claus problem. In 38th annual ACM symposium on the theory of computing (STOC) (pp. 31–40)

  • Ben-David, S., & Borodin, A. (1994). A new measure for the study of on-line algorithms. Algorithmica, 11(1), 73–91.

    Article  Google Scholar 

  • Borodin, A., Irani, S., Raghavan, P., & Schieber, B. (1995). Competitive paging with locality of reference. Journal of Computer and System Sciences, 50(2), 244–258.

    Article  Google Scholar 

  • Boyar, J., Favrholdt, L., Mikkelsen, J., & Kudahl, C. (2015). Advice complexity for a class of online problems. In 32nd international symposium on theoretical aspects of computer science (STACS), Leibniz international proceedings in informatics (Vol. 30) (pp. 116–129).

  • Boyar, J., & Favrholdt, L. M. (2007). The relative worst order ratio for on-line algorithms. ACM Transactions on Algorithms, 3(2), article 22, 24 p.

  • Boyar, J., Favrholdt, L. M., Larsen, K. S., & Nielsen, M. N. (2003). Extending the accommodating function. Acta Informatica, 40(1), 3–35.

    Article  Google Scholar 

  • Boyar, J., & Larsen, K. (1999). The seat reservation problem. Algorithmica, 25, 403–417.

    Article  Google Scholar 

  • Boyar, J., Larsen, K. S., & Nielsen, M. N. (2001). The accommodating function—A generalization of the competitive ratio. SIAM Journal on Computing, 31(1), 233–258.

    Article  Google Scholar 

  • Breslauer, D. (1998). On competitive on-line paging with lookahead. Theoretical Computer Science, 209(1–2), 365–375.

    Article  Google Scholar 

  • Chan, S. H., Lam, T. W., Lee, L. K., Liu, C. M., & Ting, H. F. (2011). Sleep management on multiple machines for energy and flow time. In L. Aceto, M. Henzinger, & J. Sgall (Eds.), Automata, languages and programming (ICALP), LNCS (Vol. 6755, pp. 219–231). Berlin: Springer.

    Chapter  Google Scholar 

  • Cho, Y., & Sahni, S. (1980). Bounds for list schedules on uniform processors. SIAM Journal on Computing, 9(1), 91–103.

    Article  Google Scholar 

  • Csirik, J., & Totik, V. (1988). On-line algorithms for a dual version of bin packing. Discrete Applied Mathematics, 21, 163–167.

    Article  Google Scholar 

  • Dorrigiv, R., López-Ortiz, A., & Munro, J. I. (2009). On the relative dominance of paging algorithms. Theoretical Computer Science, 410, 3694–3701.

    Article  Google Scholar 

  • Ehmsen, M. R., Kohrt, J. S., & Larsen, K. S. (2013). List factoring and relative worst order analysis. Algorithmica, 66(2), 287–309.

    Article  Google Scholar 

  • Epstein, L. (2005). Tight bounds for bandwidth allocation on two links. Discrete Applied Mathematics, 148(2), 181–188.

    Article  Google Scholar 

  • Epstein, L., Favrholdt, L. M., & Kohrt, J. S. (2006). Separating online scheduling algorithms with the relative worst order ratio. Journal of Combinatorial Optimization, 12(4), 363–386.

    Article  Google Scholar 

  • Epstein, L., Noga, J., Seiden, S. S., Sgall, J., & Woeginger, G. J. (2001). Randomized online scheduling on two uniform machines. Journal of Scheduling, 4(2), 71–92.

    Article  Google Scholar 

  • Giannakopoulos, Y., & Koutsoupias, E. (2015). Competitive analysis of maintaining frequent items of a stream. Theoretical Computer Science, 562, 23–32.

    Article  Google Scholar 

  • Graham, R. L. (1966). Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal, 45, 1563–1581.

    Article  Google Scholar 

  • Kalyanasundaram, B., & Pruhs, K. (2000). Speed is as powerful as clairvoyance. Journal of the ACM, 47(4), 617–643.

    Article  Google Scholar 

  • Karlin, A. R., Manasse, M. S., Rudolph, L., & Sleator, D. D. (1988). Competitive snoopy caching. Algorithmica, 3, 79–119.

    Article  Google Scholar 

  • Karlin, A. R., Phillips, S. J., & Raghavan, P. (2000). Markov paging. SIAM Journal on Computing, 30(3), 906–922.

  • Kenyon, C. (1996). Best-fit bin-packing with random order. In 7th ACM-SIAM symposium on discrete algorithms (SODA) (pp. 359–364)

  • Koutsoupias, E., & Papadimitriou, C. H. (2000). Beyond competitive analysis. SIAM Journal on Computing, 30(1), 300–317.

    Article  Google Scholar 

  • Miyazaki, S., & Okamoto, K. (2010). Improving the competitive ratios of the seat reservation problem. In 6th IFIP TC 1/WG 2.2 international conference on theoretical computer science (IFIP TCS), IFIP advances in information and communication technology (Vol. 323) (pp. 328–339). Springer.

  • Raghavan, P. (1992). A statistical adversary for on-line algorithms. In On-line algorithms, Series in discrete mathematics and theoretical computer science (Vol. 7) (pp. 79–83). American Mathematical Society.

  • Sleator, D. D., & Tarjan, R. E. (1985). Amortized efficiency of list update and paging rules. Communications of the ACM, 28(2), 202–208.

    Article  Google Scholar 

  • Woeginger, G. J. (1997). A polynomial-time approximation scheme for maximizing the minimum machine completion time. Operations Research Letters, 20(4), 149–154.

    Article  Google Scholar 

  • Young, N. (1991). Competitive paging and dual-guided algorithms for weighted caching and matching (thesis). Tech. rep. CS-TR-348-91, Computer Science Department, Princeton University.

  • Young, N. E. (1994). The \(k\)-server dual and loose competitiveness for paging. Algorithmica, 11, 525–541.

    Article  Google Scholar 

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Acknowledgements

Funding was provided by The Danish Council for Independent Research (Grant No. DFF-1323-00247) and The Villum Foundation (Grant No. VKR023219).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Joan Boyar, Lene M. Favrholdt & Kim S. Larsen

  2. Department of Mathematics, University of Haifa, Haifa, Israel

    Leah Epstein

  3. Faculty of IE&M, The Technion, Haifa, Israel

    Asaf Levin

Authors
  1. Joan Boyar
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  2. Leah Epstein
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  3. Lene M. Favrholdt
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  4. Kim S. Larsen
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  5. Asaf Levin
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Corresponding author

Correspondence to Kim S. Larsen.

Additional information

Supported in part by the Danish Council for Independent Research, Natural Sciences, and the Villum Foundation. A preliminary version of this paper appeared in the Eleventh International Computer Science Symposium in Russia, Lecture Notes in Computer Science, vol. 9691, Springer, 2016, pp. 131–145.

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Boyar, J., Epstein, L., Favrholdt, L.M. et al. Online-bounded analysis. J Sched 21, 429–441 (2018). https://doi.org/10.1007/s10951-017-0536-y

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  • DOI: https://doi.org/10.1007/s10951-017-0536-y

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