However, some definitions of transversal require that every hyperedge of the hypergraph contains precisely one vertex from the set.
Note that we get back the case of vertex covers for simple graphs if the maximum size of the hyperedges is 2.
If the maximum size of a hyperedge is restricted to d, then the problem of finding a minimum d-hitting set permits a d-approximation algorithm.
The hitting set problem is fixed-parameter tractable for the parameter OPT + d, where d is the size of the largest edge of the hypergraph.
More specifically, there is an algorithm for hitting set that runs in time d OPTnO(1).
The task is then to find a minimum cardinality subset of left-vertices which covers all of the right-vertices.
In the hitting set problem, the objective is to cover the left-vertices using a minimum subset of the right vertices.
An example of a practical application involving the hitting set problem arises in efficient dynamic detection of race condition.
This is useful in eliminating redundant write events, since large lock sets are considered unlikely in practice.
The transversal hypergraph of H is the hypergraph (X, F) whose hyperedge set F consists of all minimal-transversals of H. Computing the transversal hypergraph has applications in combinatorial optimization, in game theory, and in several fields of computer science such as machine learning, indexing of databases, the satisfiability problem, data mining, and computer program optimization.