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:
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To this favour she must come.
Bid the merchant gather wealth,
The usurer exact by stealth,
The proud man beat it from his thought,
Yet to this shape all must be brought.”
—Francis Beaumont (1584-1616)
“It is not [the toddler’s] job yet to consider other people’s feelings, he has to come to terms with his own first. If he hits you and you hit him back to “show him what it feels like,” you will have given a lesson he is not ready to learn. He will wail as if hitting was a totally new idea to him. He makes no connections between what he did to you and what you then did to him; between your feelings and his own.”
—Penelope Leach (20th century)
“My curse on plays
That have to be set up in fifty ways,
On the day’s war with every knave and dolt,
Theater business, management of men.”
—William Butler Yeats (1865–1939)