On the Smoothness of Paging Algorithms
We study the smoothness of paging algorithms. How much can the number of page faults increase due to a perturbation of the request sequence? We call a paging algorithm smooth if the maximal increase in page faults is proportional to the number of changes in the request sequence. We also introduce quantitative smoothness notions that measure the smoothness of an algorithm.
We derive lower and upper bounds on the smoothness of deterministic and randomized demand-paging and competitive algorithms. Among strongly-competitive deterministic algorithms LRU matches the lower bound, while FIFO matches the upper bound.
Well-known randomized algorithms like Partition, Equitable, or Mark are shown not to be smooth. We introduce two new randomized algorithms, called Smoothed-LRU and LRU-Random. Smoothed-LRU allows to sacrifice competitiveness for smoothness, where the trade-off is controlled by a parameter. LRU-Random is at least as competitive as any deterministic algorithm while smoother.
This work was partially supported by the DFG as part of the SFB/TR 14 AVACS.
- 12.Doyen, L., Henzinger, T., Legay, A., Nickovic, D.: Robustness of sequential circuits. In: ACSD 2010, pp. 77–84 (2010)Google Scholar
- 13.Kleene, S.: Representation of events in nerve nets and finite automata. In: Automata Studies, Princeton University Press, Princeton (1956)Google Scholar
- 15.Liu, C.L.: Some memory aspects of finite automata. Technical report 411, Massachusetts Institute of Technology, May 1963Google Scholar
- 20.Reineke, J., Salinger, A.: On the smoothness of paging algorithms, October 2015. arxiv:1510.03362