Abstract
Caching (also known as paging) is a classical problem concerning page replacement policies in two-level memory systems. General caching is the variant with pages of different sizes and fault costs. The strong NP-hardness of its two important cases, the fault model (each page has unit fault cost) and the bit model (each page has the same fault cost as size) has been established. We prove that this already holds when page sizes are bounded by a small constant: The bit and fault models are strongly NP-complete even when page sizes are limited to \(\{1, 2, 3\}\).
Considering only the decision versions of the problems, general caching is equivalent to the unsplittable flow on a path problem and therefore our results also improve the hardness results about this problem.
A full version is available on arXiv. http://arxiv.org/abs/1506.07905.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Albers, S., Arora, S., Khanna, S.: Page replacement for general caching problems. In: Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 31–40 (1999). http://dl.acm.org/citation.cfm?id=314500.314528
Bansal, N., Chakrabarti, A., Epstein, A., Schieber, B.: A quasi-PTAS for unsplittable flow on line graphs. In: Kleinberg, J.M. (ed.) Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pp. 721–729. ACM (2006). http://doi.acm.org/10.1145/1132516.1132617
Bar-Noy, A., Bar-Yehuda, R., Freund, A., Naor, J., Schieber, B.: A unified approach to approximating resource allocation and scheduling. J. ACM 48(5), 1069–1090 (2001). http://doi.acm.org/10.1145/502102.502107. A preliminary version appeared at STOC 2000
Batra, J., Garg, N., Kumar, A., Mömke, T., Wiese, A.: New approximation schemes for unsplittable flow on a path. In: Indyk, P. (ed.) Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 47–58. SIAM (2015). http://dx.doi.org/10.1137/1.9781611973730.5
Belady, L.A.: A study of replacement algorithms for a virtual-storage computer. IBM Syst. J. 5(2), 78–101 (1966). http://dx.doi.org/10.1147/sj.52.0078
Bonsma, P.S., Schulz, J., Wiese, A.: A constant-factor approximation algorithm for unsplittable flow on paths. SIAM J. Comput. 43(2), 767–799 (2014). http://dx.doi.org/10.1137/120868360
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, New York (1998)
Chrobak, M., Karloff, H.J., Payne, T.H., Vishwanathan, S.: New results on server problems. SIAM J. Discrete Math. 4(2), 172–181 (1991). http://dx.doi.org/10.1137/0404017. A preliminary version appeared at SODA 1990
Chrobak, M., Woeginger, G.J., Makino, K., Xu, H.: Caching is hard - even in the fault model. Algorithmica 63(4), 781–794 (2012). http://dx.doi.org/10.1007/s00453-011-9502-9. A preliminary version appeared at ESA 2010
Darmann, A., Pferschy, U., Schauer, J.: Resource allocation with time intervals. Theoret. Comput. Sci. 411(49), 4217–4234 (2010). http://dx.doi.org/10.1016/j.tcs.2010.08.028
Irani, S.: Page replacement with multi-size pages and applications to web caching. Algorithmica 33(3), 384–409 (2002). http://dx.doi.org/10.1007/s00453-001-0125-4. A preliminary version appeared at STOC 1997
Young, N.E.: On-line file caching. Algorithmica 33(3), 371–383 (2002). http://dx.doi.org/10.1007/s00453-001-0124-5. A preliminary version at SODA 1998
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Folwarczný, L., Sgall, J. (2015). General Caching Is Hard: Even with Small Pages. In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-662-48971-0_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48970-3
Online ISBN: 978-3-662-48971-0
eBook Packages: Computer ScienceComputer Science (R0)