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We consider the problem of online service with delay on a general metricspace, first presented by Azar, Ganesh, Ge and Panigrahi (STOC 2017). The bestknown randomized algorithm for this problem, by Azar and Touitou (FOCS 2019),is $O(\log^2 n)$-competitive, where $n$ is the number of points in the metricspace. This is also the best known result for the special case of onlineservice with deadlines, which is of independent interest.  In this paper, we present $O(\log n)$-competitive deterministic algorithmsfor online service with deadlines or delay, improving upon the results fromFOCS 2019. Furthermore, our algorithms are the first deterministic algorithmsfor online service with deadlines or delay which apply to general metric spacesand have sub-polynomial competitiveness.

Improved and Deterministic Online Service with Deadlines or Delay