  Adaptive Replacement Cache (ARC) and CLOCK with Adaptive Replacement (CAR)
are state-of-the- art "adaptive" cache replacement algorithms invented to
improve on the shortcomings of classical cache replacement policies such as
LRU, LFU and CLOCK. By separating out items that have been accessed only once
and items that have been accessed more frequently, both ARC and CAR are able to
control the harmful effect of single-access items flooding the cache and
pushing out more frequently accessed items. Both ARC and CAR have been shown to
outperform their classical and popular counterparts in practice. Both
algorithms are complex, yet popular. Even though they can be treated as online
algorithms with an "adaptive" twist, a theoretical proof of the competitiveness
of ARC and CAR remained unsolved for over a decade. We show that the
competitiveness ratio of CAR (and ARC) has a lower bound of N + 1 (where N is
the size of the cache) and an upper bound of 18N (4N for ARC). If the size of
cache offered to ARC or CAR is larger than the one provided to OPT, then we
show improved competitiveness ratios. The important implication of the above
results are that no "pathological" worst-case request sequences exist that
could deteriorate the performance of ARC and CAR by more than a constant factor
as compared to LRU.
