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42 relations: Algorithm, Backtracking, Binary relation, Bipartite graph, Computer science, Computers and Intractability, Constraint satisfaction problem, Converse relation, Cover (topology), Dancing Links, Decision problem, Depth-first search, Difference-map algorithm, Disjoint sets, Donald Knuth, Doubly linked list, Eight queens puzzle, Empty set, Function (mathematics), Heterogeneous relation, Hypergraph, Incidence matrix, Intersection (set theory), Karp's 21 NP-complete problems, Knuth's Algorithm X, List of NP-complete problems, Matching (graph theory), Mathematics, Nondeterministic algorithm, NP-completeness, Partition of a set, Pentomino, Recursion (computer science), Reduction (complexity), Restriction (mathematics), Set cover problem, Subset, Sudoku, Sudoku solving algorithms, Surjective function, Union (set theory), 3-dimensional matching.
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Backtracking
Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Bipartite graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Computers and Intractability
In computer science, more specifically computational complexity theory, Computers and Intractability: A Guide to the Theory of NP-Completeness is an influential textbook by Michael Garey and David S. Johnson.
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Constraint satisfaction problem
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations.
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Converse relation
In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation.
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Cover (topology)
In mathematics, a cover of a set X is a collection of sets whose union contains X as a subset.
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Dancing Links
In computer science, dancing links is the technique suggested by Donald Knuth to efficiently implement his Algorithm X. Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that finds all solutions to the exact cover problem.
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Decision problem
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
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Depth-first search
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures.
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Difference-map algorithm
The difference-map algorithm is a search algorithm for general constraint satisfaction problems.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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Donald Knuth
Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.
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Doubly linked list
In computer science, a doubly linked list is a linked data structure that consists of a set of sequentially linked records called nodes.
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Eight queens puzzle
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other.
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Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Heterogeneous relation
In mathematics, a heterogeneous relation is a subset of a Cartesian product A × B, where A and B are distinct sets.
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Hypergraph
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices.
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Incidence matrix
In mathematics, an incidence matrix is a matrix that shows the relationship between two classes of objects.
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Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
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Karp's 21 NP-complete problems
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.
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Knuth's Algorithm X
"Algorithm X" is the name Donald Knuth used in his paper "Dancing Links" to refer to "the most obvious trial-and-error approach" for finding all solutions to the exact cover problem.
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List of NP-complete problems
This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems.
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Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Nondeterministic algorithm
In computer science, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm.
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NP-completeness
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
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Partition of a set
In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.
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Pentomino
A pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge.
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Recursion (computer science)
Recursion in computer science is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem (as opposed to iteration).
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Reduction (complexity)
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem.
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Restriction (mathematics)
In mathematics, the restriction of a function f is a new function f\vert_A obtained by choosing a smaller domain A for the original function f. The notation f is also used.
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Set cover problem
The set cover problem is a classical question in combinatorics, computer science and complexity theory.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Sudoku
(originally called Number Place) is a logic-based, combinatorial number-placement puzzle.
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Sudoku solving algorithms
A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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3-dimensional matching
In the mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-uniform hypergraphs.
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Exact Cover, Exact cover problem, Exact hitting set.
References
[1] https://en.wikipedia.org/wiki/Exact_cover
