  In the online disjoint set covers problem, the edges of a hypergraph are
revealed online, and the goal is to partition them into a maximum number of
disjoint set covers. That is, n nodes of a hypergraph are given at the
beginning, and then a sequence of hyperedges (subsets of [n]) is presented to
an algorithm. For each hyperedge, an online algorithm must assign a color (an
integer). Once an input terminates, the gain of the algorithm is the number of
colors that correspond to valid set covers (i.e., the union of hyperedges that
have that color contains all n nodes).
  We present a deterministic online algorithm that is O(log^2 n)-competitive,
exponentially improving on the previous bound of O(n) and matching the
performance of the best randomized algorithm by Emek et al. [ESA 2019].
  For color selection, our algorithm uses a novel potential function, which can
be seen as an online counterpart of the derandomization method of conditional
probabilities and pessimistic estimators. There are only a few cases where
derandomization has been successfully used in the field of online algorithms.
In contrast to previous approaches, our result extends this tool to tackle the
following new challenges: (i) the potential function derandomizes not only the
Chernoff bound, but also the coupon collector's problem, (ii) the value of OPT
of the maximization problem is not bounded a priori, and (iii) we do not
produce a fractional solution first, but work directly on the input.
