An efficient randomized online algorithm for the paging problem for cache s
ize 2 is given, which is 3/2-competitive against an oblivious adversary. Th
e algorithm keeps track of at most one page in slow memory at any time. A l
ower bound of 37/24 approximate to 1.5416 is given for the competitiveness
of any trackless online algorithm for the same problem, i.e., an algorithm
that keeps track of no page outside the cache. (C) 2000 Elsevier Science B.
V. All rights reserved.