The k-Server with Preferences Problem
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The famous k-Server Problem covers plenty of resource allocation scenarios, and several variations have been studied extensively. However, to the best of our knowledge, no research has considered the problem if the servers are not identical and requests can express which servers should serve them. Therefore, we present a new model generalizing the k-Server Problem by preferences of the requests and study it in uniform metrics for deterministic online algorithms. In our model, requests can either demand to be answered by any server (general requests) or by a specific one (specific requests). If only general requests appear, the instance is one of the k-Server Problem, and a lower bound for the competitive ratio of k applies. If only specific requests appear, a competitive ratio of 1 becomes trivial since there is no freedom regarding the servers' movements. We show that if both kinds of requests appear, the lower bound raises to 2k-1. We study deterministic online algorithms in uniform metrics and present two algorithms. The first one has a competitive ratio dependent on the frequency of specific requests. It achieves a worst-case competitive ratio of 3k-2 while it is optimal when only general or only specific requests appear (ratio of k and 1). The second has a close-to-optimal worst-case competitive ratio of 2k+14. For the first algorithm, we show a lower bound of 3k-2, while the second one has one of 2k-1 when only general requests appear. Both algorithms differ in only one behavioral rule for each server that significantly influences the competitive ratio. Each server acting according to the rule allows approaching the worst-case lower bound, while it implies an increased lower bound for k-Server instances. Thus, there is a trade-off between performing well against instances of the k-Server Problem and ones containing specific requests.
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