Abstract
It is known that in practice, request sequences for the list update problem exhibit a certain degree of locality of reference. Motivated by this observation we apply the locality of reference model for the paging problem due to Albers et al. [STOC 2002/JCSS 2005] in conjunction with bijective analysis [SODA 2007] to list update. Using this framework, we prove that Move-to-Front (MTF) is the unique optimal algorithm for list update. This addresses the open question of defining an appropriate model for capturing locality of reference in the context of list update [Hester and Hirschberg ACM Comp. Surv. 1985]. Our results hold both for the standard cost function of Sleator and Tarjan [CACM 1985] and the improved cost function proposed independently by Martínez and Roura [TCS 2000] and Munro [ESA 2000]. This result resolves an open problem of Martínez and Roura, namely proposing a measure which can successfully separate MTF from all other list-update algorithms.
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References
Albers, S.: Improved randomized on-line algorithms for the list update problem. SIAM Journal on Computing 27(3), 682–693 (1998)
Albers, S., Favrholdt, L.M., Giel, O.: On paging with locality of reference. Journal of Computer and System Sciences 70(2), 145–175 (2005)
Albers, S., Mitzenmacher, M.: Average case analyses of list update algorithms, with applications to data compression. Algorithmica 21(3), 312–329 (1998)
Albers, S., von Stengel, B., Werchner, R.: A combined bit and timestamp algorithm for the list update problem. Information Processing Letters 56, 135–139 (1995)
Albers, S., Westbrook, J.: Self-organizing data structures. In: Fiat, A. (ed.) Dagstuhl Seminar 1996. LNCS, vol. 1442, pp. 13–51. Springer, Heidelberg (1998)
Angelopoulos, S., Dorrigiv, R., López-Ortiz, A.: On the separation and equivalence of paging strategies. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), pp. 229–237 (2007)
Bachrach, R., El-Yaniv, R.: Online list accessing algorithms and their applications: Recent empirical evidence. In: Proc. 8th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA 1997), pp. 53–62 (1997)
Becchetti, L.: Modeling locality: A probabilistic analysis of LRU and FWF. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 98–109. Springer, Heidelberg (2004)
Ben-David, S., Borodin, A.: A new measure for the study of on-line algorithms. Algorithmica 11, 73–91 (1994)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Boyar, J., Favrholdt, L.M.: The relative worst order ratio for on-line algorithms. In: Proceedings of the 5th Italian Conference on Algorithms and Complexity (2003)
Burrows, M., Wheeler, D.J.: A block-sorting lossless data compression algorithm. Technical Report 124, DEC SRC (1994)
Dorrigiv, R., López-Ortiz, A.: A survey of performance measures for on-line algorithms. SIGACT News (ACM Special Interest Group on Automata and Computability Theory) 36(3), 67–81 (2005)
El-Yaniv, R.: There are infinitely many competitive-optimal online list accessing algorithms (manuscript, 1996)
Hester, J.H., Hirschberg, D.S.: Self-organizing linear search. ACM Computing Surveys 17(3), 295 (1985)
Irani, S.: Two results on the list update problem. Information Processing Letters 38, 301–306 (1991)
Kaplan, H., Landau, S., Verbin, E.: A simpler analysis of burrows-wheeler based compression. In: Lewenstein, M., Valiente, G. (eds.) CPM 2006. LNCS, vol. 4009, pp. 282–293. Springer, Heidelberg (2006)
Martínez, C., Roura, S.: On the competitiveness of the move-to-front rule. Theoretical Computer Science 242(1–2), 313–325 (2000)
Munro, J.I.: On the competitiveness of linear search. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 338–345. Springer, Heidelberg (2000)
Reingold, N., Westbrook, J., Sleator, D.: Randomized competitive algorithms for the list update problem. Algorithmica 11, 15–32 (1994)
Schulz, F.: Two new families of list update algorithms. In: Chwa, K.-Y., H. Ibarra, O. (eds.) ISAAC 1998. LNCS, vol. 1533, pp. 99–108. Springer, Heidelberg (1998)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28, 202–208 (1985)
Torng, E.: A unified analysis of paging and caching. Algorithmica 20(2), 175–200 (1998)
I. H. Witten and T. Bell. The Calgary/Canterbury text compression corpus. Anonymous ftp from: ftp.cpsc.ucalgary.ca/pub/text.compression/corpus/text.compression.corpus.tar.Z
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Angelopoulos, S., Dorrigiv, R., López-Ortiz, A. (2008). List Update with Locality of Reference. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_35
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DOI: https://doi.org/10.1007/978-3-540-78773-0_35
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