Abstract
This paper addresses the page migration problem: given online requests from nodes on a network for accessing a page stored in a node, to output online migrations of the page. Serving a request costs the distance between the request and the page, and migrating the page costs the migration distance multiplied by the page size D ≥ 1. The objective is to minimize the total sum of service costs and migration costs. Black and Sleator conjectured that there exists a 3-competitive deterministic algorithm for every graph. Although the conjecture was disproved for the case D = 1, whether or not an asymptotically (with respect to D) 3-competitive deterministic algorithm exists for every graph is still open. In fact, we did not know if there exists a 3-competitive deterministic algorithm for an extreme case of three nodes with D ≥ 2. As the first step toward an asymptotic version of the Black and Sleator conjecture, we present 3- and (3 + 1/D)-competitive algorithms on three nodes with D = 2 and D ≥ 3, respectively, and a lower bound of 3 + Ω(1/D) that is greater than 3 for every D ≥ 3. In addition to the results on three nodes, we also derive ρ-competitiveness on complete graphs with edge-weights between 1 and 2 − 2/ρ for any ρ ≥ 3, improving the previous 3-competitive algorithm on uniform networks.
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References
Awerbuch, B., Bartal, Y., Fiat, A.: Distributed paging for general networks. J. Algorithms 28(1), 67–104 (1998)
Awerbuch, B., Bartal, Y., Fiat, A.: Competitive distributed file allocation. Information and Computation 185(1), 1–40 (2003)
Bartal, Y., Charikar, M., Indyk, P.: On page migration and other relaxed task systems. Theoret. Comput. Sci. 268(1), 43–66 (2001)
Bartal, Y., Fiat, A., Rabani, Y.: Competitive algorithms for distributed data management. J. Comput. Sys. Sci. 51(3), 341–358 (1995)
Bein, W.W., Chrobak, M., Larmore, L.L.: The 3-server problem in the plane. Theoret. Comput. Sci. 289, 335–354 (2002)
Bienkowski, M.: Migrating and replicating data in networks. Comput. Sci. Res. Dev. (2011), doi:10.1007/s00450-011-0150-8
Bienkowski, M., Byrka, J., Korzeniowski, M., Meyer auf der Heide, F.: Optimal algorithms for page migration in dynamic networks. J. Discrete Algorithms 7(4), 545–569 (2009)
Black, D.L., Sleator, D.D.: Competitive algorithms for replication and migration problems. Tech. Rep. CMU-CS-89-201, Department of Computer Science, Carnegie Mellon University (1989)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)
Chrobak, M., Larmore, L.L., Reingold, N., Westbrook, J.: Page migration algorithms using work functions. J. Algorithms 24(1), 124–157 (1997)
Karlin, A., Manasse, M., Rudolph, L., Sleator, D.: Competitive snoopy caching. Algorithmica 3(1), 79–119 (1988)
Koutsoupias, E., Papadimitriou, C.: On the k-server conjecture. J. ACM 42, 971–983 (1995)
Lund, C., Reingold, N., Westbrook, J., Yan, D.: Competitive on-line algorithms for distributed data management. SIAM J. Comput. 28(3), 1086–1111 (1999)
Matsubayashi, A.: Uniform page migration on general networks. International Journal of Pure and Applied Mathematics 42(2), 161–168 (2007)
Westbrook, J.: Randomized algorithms for multiprocessor page migration. In: DIMACS. Discrete Mathematics and Theoretical Computer Science, vol. 7, pp. 135–150 (1992)
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Matsubayashi, A. (2013). Asymptotically Optimal Online Page Migration on Three Points. In: Erlebach, T., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2012. Lecture Notes in Computer Science, vol 7846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38016-7_10
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DOI: https://doi.org/10.1007/978-3-642-38016-7_10
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