  Online algorithms process their inputs piece by piece, taking irrevocable
decisions for each data item. This model is too restrictive for most
partitioning problems, since data that is yet to arrive may render it
impossible to extend partial partitionings to the entire data set reasonably
well.
  In this work, we show that preemption might be a potential remedy. We
consider the problem of partitioning online sequences, where $p-1$ separators
need to be inserted into a sequence of integers that arrives online so as to
create $p$ contiguous partitions of similar weight. While without preemption no
algorithm with non-trivial competitive ratio is possible, if preemption is
allowed, i.e., inserted partition separators may be removed but not reinserted
again, then we show that constant competitive algorithms can be obtained. Our
contributions include:
  We first give a simple deterministic $2$-competitive preemptive algorithm for
arbitrary $p$ and arbitrary sequences. Our main contribution is the design of a
highly non-trivial partitioning scheme, which, under some natural conditions
and $p$ being a power of two, allows us to improve the competitiveness to
$1.68$. We also show that the competitiveness of deterministic (randomized)
algorithms is at least $\frac{4}{3}$ (resp. $\frac{6}{5}$).
  For $p=2$, the problem corresponds to the interesting special case of
preemptively guessing the center of a weighted request sequence. While
deterministic algorithms fail here, we provide a randomized $1.345$-competitive
algorithm for all-ones sequences and prove that this is optimal. For weighted
sequences, we give a $1.628$-competitive algorithm and a lower bound of $1.5$.
