关于时间最优k服务器问题的离线版本

中文摘要 AI 辅助

我们考虑k个相同移动资源的并行重新定位的离线问题。在每个预先已知的请求之后，资源可以同时移动，一步的持续时间由最长的单个移动决定。该模型等价于时间最优k服务器问题的离线版本。我们证明，即使在欧几里得直线的有限子集的度量上，或等价地在加权路径的顶点度量上，决策版本已经是强NP完全的。因此，即使在允许的资源位置呈线性排列的情况下，计算难度仍然存在。作为一个积极的结果，我们表明，在具有通用顶点的无向无权图的度量上，该问题可以在多项式时间内精确求解。

英文摘要

We consider the offline problem of parallel relocation of k identical mobile resources. After each request, known in advance, the resources may move simultaneously, and the duration of a step is determined by the longest individual movement. This model is equivalent to the offline version of the time-optimal k-server problem. We prove that the decision version is strongly NP-complete already on metrics of finite subsets of the Euclidean line, or equivalently, on vertex metrics of weighted paths. Thus, the computational hardness persists even under a linear arrangement of the admissible resource locations. As a positive result, we show that the problem can be solved exactly in polynomial time on metrics of undirected unweighted graphs with a universal vertex.

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• GoodsForecast

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