  A hypergraph ${\cal F}$ is a set family defined on vertex set $V$. The dual
of ${\cal F}$ is the set of minimal subsets $H$ of $V$ such that $F\cap H \ne
\emptyset$ for any $F\in {\cal F}$. The computation of the dual is equivalent
to many problems, such as minimal hitting set enumeration of a subset family,
minimal set cover enumeration, and the enumeration of hypergraph transversals.
Although many algorithms have been proposed for solving the problem, to the
best of our knowledge, none of them can work on large-scale input with a large
number of output minimal hitting sets. This paper focuses on developing time-
and space-efficient algorithms for solving the problem. We propose two new
algorithms with new search methods, new pruning methods, and fast techniques
for the minimality check. The computational experiments show that our
algorithms are quite fast even for large-scale input for which existing
algorithms do not terminate in a practical time.
