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In this work, we are interested in the problem of satisfying multiple concurrent requests submitted to a computing server. Informally, there are users each sending a sequence of requests to the server. The requests consist of tasks linked by precedence constraints. Tasks may occur several times in the same sequence as well as in a request sequence of another user. The computing server has to execute tasks with variable processing times. The server owns a cache of limited size where intermediate results of the processing may be stored. If an intermediate result for a task is stored into the cache, no processing cost has to be paid and the result can directly be fetched from the cache. The goal of this work is to determine a schedule of the tasks such that an optimization function is minimized (the only objective studied up to now is the makespan). This problem is a variant of caching which considers only one sequence of requests. We then extend the study to the minimization of the mean completion time of the request sequences. Two models are considered. In the ?rst model, caching is forced whereas in the second model caching is optional and one can choose whether an intermediate result is stored in the cache or not. All combinations turn out to be NP-hard for ?xed cache sizes and we provide a formulation as dynamic program as well as bounds for inapproximation. We propose polynomial time approximation algorithms for some variants and analyze their approximation ratios. Finally, we also devise some heuristics and present experimental results.

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