In mathematics, given a collection of subsets of a set X, an exact cover is a subcollection of such that each element in X is contained in exactly one subset in . One says that each element in X is covered by exactly one subset in . An exact cover is a kind of cover.
In computer science, the exact cover problem is a decision problem to find an exact cover or else determine none exists. The exact cover problem is NP-complete and is one of Karp's 21 NP-complete problems. The exact cover problem is a kind of constraint satisfaction problem.
An exact cover problem can be represented by an incidence matrix or a bipartite graph.
Knuth's Algorithm X is an algorithm that finds all solutions to an exact cover problem. Dancing Links, commonly known as DLX, is the technique suggested by Donald Knuth to efficiently implement his Algorithm X on a computer.
The standard exact cover problem can be generalized slightly to involve not only "exactly one" constraints but also "at-most-one" constraints.
Finding Pentomino tilings and solving Sudoku are noteworthy examples of exact cover problems. The N queens problem is a slightly generalized exact cover problem.
Read more about Exact Cover: Formal Definition, Representations, Equivalent Problems, Exact Hitting Set, Finding Solutions, Generalizations, Noteworthy Examples
Famous quotes containing the words exact and/or cover:
“His eye had become minutely exact as to the book and its position. Then he resolved that he would not look at the book again, would not turn a glance on it unless it might be when he had made up his mind to reveal its contents.”
—Anthony Trollope (1815–1882)
“Nothing can we call our own but death,
And that small model of the barren earth
Which serves as paste and cover to our bones.”
—William Shakespeare (1564–1616)