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In the mathematical field of topology, given a collection S of subsets of a set X, an exact cover is a subcollection S of S such that each element in X is contained in exactly one subset in S. One says that each element in X is covered by exactly one subset in S. An exact cover is a kind of cover.
In computer science, the exact cover problem is a decision problem to determine if an exact cover exists. The exact cover problem is NP-complete and is one of Karp's 21 NP-complete problems. It is NP-complete even when each subset in S contains exactly three elements; this restricted problem is known as exact cover by 3-sets, often abbreviated X3C. 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. DLX is the name given to Algorithm X when it is implemented efficiently using Donald Knuth's Dancing Links technique on a computer.