  This paper provides an algorithmic framework for obtaining fast distributed
algorithms for a highly-dynamic setting, in which *arbitrarily many* edge
changes may occur in each round. Our algorithm significantly improves upon
prior work in its combination of (1) having an $O(1)$ amortized time
complexity, (2) using only $O(\log{n})$-bit messages, (3) not posing any
restrictions on the dynamic behavior of the environment, (4) being
deterministic, (5) having strong guarantees for intermediate solutions, and (6)
being applicable for a wide family of tasks.
  The tasks for which we deduce such an algorithm are maximal matching,
$(degree+1)$-coloring, 2-approximation for minimum weight vertex cover, and
maximal independent set (which is the most subtle case). For some of these
tasks, node insertions can also be among the allowed topology changes, and for
some of them also abrupt node deletions.
