  Online algorithms make decisions based on past inputs. In general, the
decision may depend on the entire history of inputs. If many computers run the
same online algorithm with the same input stream but are started at different
times, they do not necessarily make consistent decisions.
  In this work we introduce time-local online algorithms. These are online
algorithms where the output at a given time only depends on $T = O(1)$ latest
inputs. The use of (deterministic) time-local algorithms in a distributed
setting automatically leads to globally consistent decisions.
  Our key observation is that time-local online algorithms (in which the output
at a given time only depends on local inputs in the temporal dimension) are
closely connected to local distributed graph algorithms (in which the output of
a given node only depends on local inputs in the spatial dimension). This makes
it possible to interpret prior work on distributed graph algorithms from the
perspective of online algorithms.
  We describe an algorithm synthesis method that one can use to design optimal
time-local online algorithms for small values of $T$. We demonstrate the power
of the technique in the context of a variant of the online file migration
problem, and show that e.g. for two nodes and unit migration costs there exists
a $3$-competitive time-local algorithm with horizon $T=4$, while no
deterministic online algorithm (in the classic sense) can do better. We also
derive upper and lower bounds for a more general version of the problem; we
show that there is a $6$-competitive deterministic time-local algorithm and a
$2.62$-competitive randomized time-local algorithm for any migration cost
$\alpha \ge 1$.

Data Structures and Algorithms;Distributed, Parallel, and Cluster Computing