最小化拒绝的接纳控制和具有重复的在线集合覆盖
Admission Control to Minimize Rejections and Online Set Cover with Repetitions
摘要：
我们研究一般网络中的接纳控制问题。通信请求随着时间的推移而到达，在线算法接受或拒绝每个请求，同时保持网络的容量限制。准入控制问题通常被分析为一个效益问题，其目标是设计一个在线算法，以接受最大数量的请求。该目标函数的问题在于，即使具有最佳竞争比的算法也可能拒绝几乎所有请求，而实际上只能拒绝少数请求。这可能不适用于拒绝是罕见事件的情况。在本文中，我们考虑抢占式的在线算法，其目标是最大限度地减少拒绝请求的数量。每个请求到达一起的路径，它应该被routedon. We示出了一个$O(\log^2 (mc))$的竞争随机算法的加权情况下，其中$m$是在图中的边缘的数量和$c$是最大的边缘容量。对于未加权的情形，我们给出了一个$O(\log m \log c)$ -竞争随机算法.这解决了Blum、Kalai和Kleinberg在\cite{BlKaKl01}中提出的一个未决问题。我们注意到，允许抢占和处理具有给定路径的请求对于避免平凡的下限是必不可少的。
英文摘要：
We study the admission control problem in general networks. Communication requests arrive over time, and the online algorithm accepts or rejects each request while maintaining the capacity limitations of the network. The admission control problem has been usually analyzed as a benefit problem, where the goal is to devise an online algorithm that accepts the maximum number of requests possible. The problem with this objective function is that even algorithms with optimal competitive ratios may reject almost all of the requests, when it would have been possible to reject only a few. This could be inappropriate for settings in which rejections are intended to be rare events. In this paper, we consider preemptive online algorithms whose goal is to minimize the number of rejected requests. Each request arrives together with the path it should be routed on. We show an $O(\log^2 (mc))$-competitive randomized algorithm for the weighted case, where $m$ is the number of edges in the graph and $c$ is the maximum edge capacity. For the unweighted case, we give an $O(\log m \log c)$-competitive randomized algorithm. This settles an open question of Blum, Kalai and Kleinberg raised in \cite{BlKaKl01}. We note that allowing preemption and handling requests with given paths are essential for avoiding trivial lower bounds.
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