In mathematics, given a collection of subsets of a set X, an exact hitting set X* is a subset of X such that each subset in contains exactly one element in X*. One says that each subset in is hit by exactly one element in X*.
In computer science, the exact hitting set problem is a decision problem to find an exact hitting set or else determine none exists.
The exact hitting set problem is an abstract exact cover problem. In the notation above, P is the set X, Q is a collection of subsets of X, R is the binary relation "is contained in" between elements and subsets, and R -1 restricted to Q × P* is the function "contains" from subsets to selected elements.
Whereas an exact cover problem involves selecting subsets and the relation "contains" from subsets to elements, an exact hitting set problem involves selecting elements and the relation "is contained in" from elements to subsets. In a sense, an exact hitting set problem is the inverse of the exact cover problem involving the same set and collection of subsets.
Read more about this topic: Exact Cover
Famous quotes containing the words exact, hitting and/or set:
“To conclude, The Light of humane minds is Perspicuous Words, but by exact definitions first snuffed, and purged from ambiguity; Reason is the pace; Encrease of Science, the way; and the Benefit of man-kind, the end.”
—Thomas Hobbes (1579–1688)
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—Penelope Leach (20th century)
“Dreamer of dreams, born out of my due time,
Why should I strive to set the crooked straight?
Let it suffice me that my murmuring rhyme
Beats with light wing against the ivory gate,”
—William Morris (1834–1896)