The Multi-threaded Paging problem (MTP) generalizes Paging to the case where there are many threads of requests. This models situations in which the requests come from more than one independent source. At each step it is necessary to decide which request to serve, and also (as in normal Paging) which page of fast memory to remove on a page fault. In MTP the input sequences are allowed to be either finite or infinite, and the problem is considered both with and without a fairness constraint on the way in which the individual requests are served. In this paper we propose alternative definitions of competitiveness for deterministic on-line algorithms for the infinite versions of MTP. The new definitions intend to compare the algorithms' steady-state performances on infinite sequences. Although a priori the alternative definitions seem different, we find that they are essentially equivalent. This suggests that the somehow negative results obtained when MTP was introduced, may be consider...

Contents iii Contents 1 Cover Page i 2 Project Summary ii 3 Table of Contents iii 4 Objectives and Aims 1 5 Narrative and Bibliography 2 5.1 Rationale of the Project . . . . . . . . . . . . . . . . . . . . . . . . . 2 5.1.1 Current Status . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5.1.2 Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5.1.3 Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5.2 Research Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5.2.1 NP-Hard Problems . . . . . . . . . . . . . . . . . . . . . . . . 4 5.2.2 Online Problems . . . . . . . . . . . . . . . . . . . . . . . . . 5 5.2.3 Approximation Algorithms . . . . . . . . . . . . . . . . . . . . 6 5.2.4 Previous and Ongoing Work . . . . . . . . . . . . . . . . . . . 7 5.2.5 Planned Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2.6 Plans for Publication . . . . . . . . . . . . .

Traditionally, on-line problems have been studied under the assumption that there is a unique sequence of requests that must be served. This approach is common to most general models of on-line computation, such as Metrical Task Systems. However, there exist on-line problems in which the requests are organized in more than one independent thread. In this more general framework, at every moment the first unserved request of each thread is available. Therefore, apart from deciding how to serve a request, at each stage it is necessary to decide which request to serve among several possibilities. In this paper we introduce Multi-threaded Metrical Task Systems, that is, the generalization of Metrical Task Systems to the case in which there are many threads of tasks. We study the problem from a competitive analysis point of view, proving lower and upper bounds on the competitiveness of on-line algorithms. We consider finite and infinite sequences of tasks, as well as deterministic and ran...