Theory Comput Syst (2018) 62:366–418
On the Smoothness of Paging Algorithms
· Alejandro Salinger
Published online: 13 October 2017
© Springer Science+Business Media, LLC 2017
Abstract We study the smoothness of paging algorithms. How much can the num-
ber 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 smooth-
ness 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 such as P
are shown not
to be smooth. We introduce two new randomized algorithms, called S
LRU and LRU-R
-LRU allows sacrificing competitiveness for
This work was partially supported by the German Research Council (DFG) as part of the project
“PEP: Precise and Efficient Prediction of Good Worst-case Performance for Contemporary and
Future Architectures” and as part of the Transregional Collaborative Research Center “Automatic
Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS).
We would like to sincerely thank the anonymous reviewers for their help in improving this paper.
Most of the reported work was carried out while the second author was a postdoctoral researcher
at Saarland University.
A preliminary version of this work appeared at the 13th Workshop on Approximation and Online
Algorithms (WAOA) .
Department of Computer Science, Saarland University, Saarbr
SAP SE, Walldorf, Germany