Online Service with Delay on a Line

  • Marcin BienkowskiEmail author
  • Artur Kraska
  • Paweł Schmidt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11085)


In the Online Service with Delay (OSD) problem, introduced recently by Azar et al. (STOC 2017), there are an n-point metric space and a server occupying some point. Points request service over time and these requests need to be eventually served by moving the server to these points. To exploit spatial locality of requests, a service may be delayed and requests may be served in batches. However, there are certain penalties associated with the delays, e.g., such penalty may be proportional to the waiting time of a given request. The goal is to minimize the sum of the total distance traveled by the server and all delay penalties. The OSD problem is closely related to widely studied optimization problems, such as the reordering buffer management and the multi-level aggregation. Azar et al. (STOC 2017) gave a randomized online \(O(\log ^4 n)\)-competitive algorithm for general metric spaces. In this paper, we present a deterministic \(O(\log n)\)-competitive algorithm for the case when the metric space is a line consisting of n equidistant points.


Delayed service Server problems Online algorithms Competitive analysis 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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