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Competitive algorithms for server problems. (English) Zbl 0705.68023

Summary: The k-server problem is that of planning the motion of k mobile servers on the vertices of a graph under a sequence of requests for service. Each request consists of the name of a vertex, and is satisfied by placing a server at the requested vertex. The requests must be satisfied in their order of occurrence. The cost of satisfying a sequence of requests is the distance moved by the servers. We study on-line algorithms for this problem from the competitive point of view. That is, we seek to develop on-line algorithms whose performance on any sequence of requests is as close as possible to the performance of the optimum off-line algorithm. We obtain optimally competitive algorithms for several important cases. Because of the flexibility in choosing the distances in the graph and the number of servers, the k-server problem can be used to model a number of important paging and caching problems. It can also be used as a building block for solving more general problems. We show how server algorithms can be used to solve a seemingly more general class of problems known as task systems.

MSC:

68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
68R10 Graph theory (including graph drawing) in computer science
90B35 Deterministic scheduling theory in operations research
68W10 Parallel algorithms in computer science
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