Abstract
The classical paging problem is to maintain a two-level memory system so that a sequence of requests to memory pages can be served with a small number of faults. Standard competitive analysis gives overly pessimistic results as it ignores the fact that real-world input sequences exhibit locality of reference. In this paper we study the paging problem using an intuitive and simple locality model that records inter-request distances in the input. A characteristic vector \(\mathcal{C}\) defines a class of request sequences that satisfy certain properties on these distances. The concept was introduced by Panagiotou and Souza [19].
As a main contribution we develop new and improved bounds on the performance of important paging algorithms. A strength and novelty of the results is that they express algorithm performance in terms of locality parameters. In a first step we develop a new lower bound on the number of page faults incurred by an optimal offline algorithm opt. The bound is tight up to a small additive constant. Based on these expressions for opt’s cost, we obtain nearly tight upper and lower bounds on lru’s competitiveness, given any characteristic vector \(\mathcal{C}\). The resulting ratios range between 1 and \(k\), depending on \(\mathcal{C}\). Furthermore, we compare lru to fifo and fwf. For the first time we show bounds that quantify the difference between lru’s performance and that of the other two strategies. The results imply that lru is strictly superior on inputs with a high degree of locality of reference. In particular, there exist general input families for which lru achieves constant competitive ratios whereas the guarantees of fifo and fwf tend to \(k\), the size of the fast memory. Finally, we report on an experimental study that demonstrates that our theoretical bounds are very close to the experimentally observed ones. Hence we believe that our contributions bring competitive paging again closer to practice.
Susanne Albers Work supported by the German Research Foundation, grant Al 464/7-1.
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Albers, S., Favrholdt, L.M., Giel, O.: On paging with locality of reference. J. Comput. Syst. Sci. 70(2), 145–175 (2005)
Angelopoulos, S., Dorrigiv, R., López-Ortiz, A.: On the separation and equivalence of paging strategies. In: Proc. 18th ACM-SIAM SODA, pp. 229–237 (2007)
Angelopoulos, S., Schweitzer, P.: Paging and list update under bijective analysis. J. ACM 60(2), 7 (2013)
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(1), 73–91 (1994)
Boyar, J., Favrholdt, L.M., Larsen, K.S.: The relative worst-order ratio applied to paging. J. Comput. Syst. Sci. 73(5), 818–843 (2007)
Boyar, J., Gupta, S., Larsen, K.S.: Access graphs results for LRU versus FIFO under relative worst order analysis. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 328–339. Springer, Heidelberg (2012)
Boyar, J., Gupta, S., Larsen, K.S.: Relative interval analysis of paging algorithms on access graphs. In: Dehne, F., Solis-Oba, R., Sack, J.-R. (eds.) WADS 2013. LNCS, vol. 8037, pp. 195–206. Springer, Heidelberg (2013)
Borodin, A., Irani, S., Raghavan, P., Schieber, B.: Competitive paging with locality of reference. J. Comput. Syst. Sci. 50, 244–258 (1995)
Dorrigiv, R., Ehmsen, M.R., López-Ortiz, A.: Parameterized analysis of paging and list update algorithms. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 104–115. Springer, Heidelberg (2010)
Dorrigiv, R., López-Ortiz, A.: On developing new models, with paging as a case study. SIGACT News 40(4), 98–123 (2009)
Chrobak, M., Noga, J.: LRU is better than FIFO. Algorithmica 23, 180–185 (1999)
Dorrigiv, R., López-Ortiz, A., Munro, J.I.: On the relative dominance of paging algorithms. Theor. Comput. Sci. 410(38–40), 3694–3701 (2009)
S. Kaplan. Trace reduction for virtual memory simulation. Benchmark library at https://www3.amherst.edu/~sfkaplan/research/trace-reduction/
Kaplan, S.F., Smaragdakis, Y., Wilson, P.R.: Trace reduction for virtual memory simulations. In: Proc. International ACM SIGMETRICS Conference, pp. 47–58 (1999)
Karlin, A., Phillips, S., Raghavan, P.: Markov paging. SIAM J. Comput. 30(3), 906–922 (2000)
Koutsoupias, E., Papadimitriou, C.H.: Beyond competitive analysis. SIAM J. Comput. 30(1), 300–317 (2000)
Irani, S., Karlin, A.R., Phillips, S.: Strongly competitive algorithms for paging with locality of reference. SIAM J. Comput. 25, 477–497 (1996)
Panagiotou, K., Souza, A.: On adequate performance measures for paging. In: Proc. 38th Annual ACM Symposium on Theory of Computing (STOC), pp. 487–496 (2006)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28, 202–208 (1985)
Young, N.E.: The \(k\)-server dual and loose competitiveness for paging. Algorithmica 11, 525–541 (1994)
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Albers, S., Frascaria, D. (2015). Quantifying Competitiveness in Paging with Locality of Reference. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_3
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