  The notion of age of information (AoI) has become an important performance
metric in network and control systems. Information freshness, represented by
AoI, naturally arises in the context of caching. We address optimal scheduling
of cache updates for a time-slotted system where the contents vary in size.
There is limited capacity for the cache and for making content updates. Each
content is associated with a utility function that is monotonically decreasing
in the AoI. For this combinatorial optimization problem, we present the
following contributions. First, we provide theoretical results settling the
boundary of problem tractability. In particular, by a reformulation using
network flows, we prove the boundary is essentially determined by whether or
not the contents are of equal size. Second, we derive an integer linear
formulation for the problem, of which the optimal solution can be obtained for
small-scale scenarios. Next, via a mathematical reformulation, we derive a
scalable optimization algorithm using repeated column generation. In addition,
the algorithm computes a bound of global optimum, that can be used to assess
the performance of any scheduling solution. Performance evaluation of
large-scale scenarios demonstrates the strengths of the algorithm in comparison
to a greedy schedule. Finally, we extend the applicability of our work to
cyclic scheduling.
