Serving Online Requests with Mobile Servers
We study an online problem in which mobile servers have to be moved in order to efficiently serve at set of online requests. More formally, there is a set of n nodes and a set of k mobile servers that are placed at some of the nodes. Each node can potentially host several servers and the servers can be moved between the nodes. There are requests \(1,2,\ldots \) that are adversarially issued at nodes one at a time, where a request issued at time t needs to be served at all times \(t' \ge t\). The cost for serving the requests is a function of the number of servers and requests at the different nodes. The requirements on how to serve the requests are governed by two parameters \(\alpha \ge 1\) and \(\beta \ge 0\). An algorithm needs to guarantee that at all times, the total service cost remains within a multiplicative factor \(\alpha \) and an additive term \(\beta \) of the current optimal service cost.
We consider online algorithms for two different minimization objectives. We first consider the natural problem of minimizing the total number of server movements. We show that in this case for every k, the competitive ratio of every deterministic online algorithm needs to be at least \(\varOmega (n)\). Given this negative result, we then extend the minimization objective to also include the current service cost. We give almost tight bounds on the competitive ratio of the online problem where one needs to minimize the sum of the total number of movements and the current service cost. In particular, we show that at the cost of an additional additive term which is roughly linear in k, it is possible to achieve a multiplicative competitive ratio of \(1+\varepsilon \) for every constant \(\varepsilon >0\).
KeywordsMovement minimization Competitive analysis General cost function
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