In the reordering buffer management problem a sequence of requests arrive online in a finite metric space, and have to be processed by a single server. This server is equipped with a request buffer of size k and can decide at each point in time, which request from its buffer to serve next. Servicing of a request is simply done by moving the server to the location of the request. The goal is to process all requests while minimizing the total distance that the server is traveling inside the metric space.In this paper we present a deterministic algorithm for the reordering buffer management problem that achieves a competitive ratio of O(log Delta + min {log n,log k}) in a finite metric space of n points and aspect ratio Delta. This is the first algorithm that works for general metric spaces and has just a logarithmic dependency on the relevant parameters. The guarantee is memory-robust, i.e., the competitive ratio decreases only slightly when the buffer-size of the optimum is increased to h=(1+epsilon)k. For memory robust guarantees our bounds are close to optimal.
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