A note on the complexity of the causal ordering problem
  In this note we provide a concise report on the complexity of the causal
ordering problem, originally introduced by Simon to reason about causal
dependencies implicit in systems of mathematical equations. We show that
Simon's classical algorithm to infer causal ordering is NP-Hard---an
intractability previously guessed but never proven. We present then a detailed
account based on Nayak's suggested algorithmic solution (the best available),
which is dominated by computing transitive closure---bounded in time by
$O(|\mathcal V|\cdot |\mathcal S|)$, where $\mathcal S(\mathcal E, \mathcal V)$
is the input system structure composed of a set $\mathcal E$ of equations over
a set $\mathcal V$ of variables with number of variable appearances (density)
$|\mathcal S|$. We also comment on the potential of causal ordering for
emerging applications in large-scale hypothesis management and analytics.
