This thesis is concerned with caching algorithms. We investigate three variations of the caching problem: web caching in the Torng framework, relative competitiveness and caching with request reordering.
In the first variation we define different cost models involving page sizes and page costs. We also present the Torng cost framework introduced by Torng in [29]. Next we analyze the competitive ratio of online deterministic marking algorithms in the BIT cost model combined with the Torng framework. We show that given some specific restrictions on the set of possible request sequences, any marking algorithm is 2-competitive.
The second variation consists in using the relative competitiveness ratio on an access graph as a complexity measure. We use the concept of access graphs introduced by Borodin [11] to define our own concept of relative competitive ratio. We demonstrate results regarding the relative competitiveness of two cache eviction policies in both the basic and the Torng framework combined with the CLASSICAL cost model.
The third variation is caching with request reordering. Two reordering models are defined. We prove some important results about the value of a move and number of orderings, then demonstrate results about the approximation factor and competitive ratio of offline and online reordering schemes, respectively.
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