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Algorithm that outputs all solutions to a problem
computer science, an enumeration algorithm is an algorithm that enumerates the answers to a computational problem. Formally, such an algorithm applies to problems
Enumeration_algorithm
Algorithmic paradigm for constraint satisfaction or enumeration problems
Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction or enumeration problems, that incrementally
Backtracking
Mathematical logic concept
an algorithm such that the set of input numbers for which the algorithm halts is exactly S. Or, equivalently, There is an algorithm that enumerates the
Computably_enumerable_set
Algorithm for listing maximal cliques
In computer science, the Bron–Kerbosch algorithm is an enumeration algorithm for finding all maximal cliques in an undirected graph. That is, it lists
Bron–Kerbosch_algorithm
Ordered listing of items in collection
of mathematics concerned with enumerating in this sense. For instance, in partition enumeration and graph enumeration the objective is to count partitions
Enumeration
Sequence of operations for a task
category also includes search algorithms, branch and bound enumeration, and backtracking. Randomized algorithm Such algorithms make some choices randomly
Algorithm
Tarjan's algorithm may refer to one of several algorithms attributed to Robert Tarjan, including: Tarjan's strongly connected components algorithm Tarjan's
Tarjan's_algorithm
are not allowed to say "run the enumeration algorithm until...". However, we can say "run the enumeration algorithm for up to k steps", provided that
Craig's_theorem
Optimization by removing non-optimal solutions to subproblems
brute-force enumeration of candidate solutions and testing them all. To improve on the performance of brute-force search, a B&B algorithm keeps track
Branch_and_bound
Method of finding a directed graph's strongly connected components
the original graph. The primitive graph operations that the algorithm uses are to enumerate the vertices of the graph, to store data per vertex (if not
Kosaraju's_algorithm
Algorithm for solving the coset enumeration problem
the Todd–Coxeter algorithm, created by J. A. Todd and H. S. M. Coxeter in 1936, is an algorithm for solving the coset enumeration problem. Given a presentation
Todd–Coxeter_algorithm
Combinatorial algorithm
calls it "perhaps the most prominent permutation enumeration algorithm". A version of the algorithm can be implemented in such a way that the average
Steinhaus–Johnson–Trotter algorithm
Steinhaus–Johnson–Trotter_algorithm
bounding inequalities given the vertices is called facet enumeration (see convex hull algorithms). The computational complexity of the problem is a subject
Vertex_enumeration_problem
Database theory algorithm
O(|Q||D||OUT|)} . The algorithm has been influential in database theory and its core ideas are found in algorithms for other tasks such as enumeration and aggregate
Yannakakis_algorithm
finite order, coset enumeration gives the order of G as well. For small groups it is sometimes possible to perform a coset enumeration by hand. However,
Coset_enumeration
Algorithm to search the nodes of a graph
exists, and be ∞ otherwise. Let σ=(v1,…,vn) be an enumeration of the vertices of V. The enumeration σ is said to be a BFS ordering (with source v1) if
Breadth-first_search
ideals. Avis, David; Fukuda, Komei (1992), "A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra", Discrete & Computational
Reverse-search_algorithm
Optimal Join Algorithms, Enumeration, Factorization, Ranking, and Dynamic Programming". ICDE 2022 Tutorial. Part 3: Acyclic queries & Enumeration. Slides,
GYO_algorithm
Unsolved problem in computer science
polynomial function on the size of the input to the algorithm. The general class of questions that some algorithm can answer in polynomial time is "P" or "class
P_versus_NP_problem
Type of sub-graph
an algorithm named RAND-ESU that provides a significant improvement over mfinder. This algorithm, which is based on the exact enumeration algorithm ESU
Network_motif
enumeration-reducible to B if an enumeration of B can be algorithmically converted to an enumeration of A. In particular, if B is computably enumerable, then A also is
Enumeration_reducibility
Halting probability of a random computer program
In the computer science subfield of algorithmic information theory, a Chaitin constant, Chaitin omega number, or halting probability is a real number
Chaitin's_constant
Combinatorial algorithm
{\bigl (}u,i+1,g-c(v_{i}u){\bigr )}} onto the stack. Stop As an enumeration algorithm this is slightly flawed, because it may report the same trail multiple
Lin–Kernighan_heuristic
Software inventory list
cryptographic assets present in a software, firmware, device, or system. It enumerates algorithms (and parameters such as key sizes and modes), cryptographic libraries
Cryptographic bill of materials
Cryptographic_bill_of_materials
In the analysis of algorithms, an enumeration algorithm (i.e., an algorithm for listing a large or infinite collection of structures) is said to have polynomial
Polynomial_delay
Formal language
function) which will enumerate all valid strings of the language. Note that if the language is infinite, the enumerating algorithm provided can be chosen
Recursively enumerable language
Recursively_enumerable_language
Property describing run-time complexity of algorithms
output-sensitive algorithms are enumeration algorithms, which enumerate the set of solutions to a problem. In this context, the performance of algorithms is also
Output-sensitive_algorithm
Class of mathematical functions
specialized techniques for optimizing submodular functions. Theory and enumeration algorithms for finding local and global maxima (minima) of submodular (supermodular)
Supermodular_function
Philosphical view that existence proofs must be constructive
functions range, and thereby establishes a contradiction. One can enumerate algorithms to construct a function T, about which we initially assume that it
Constructivism (philosophy of mathematics)
Constructivism_(philosophy_of_mathematics)
Algorithm for virtual memory implementation
system that uses paging for virtual memory management, page replacement algorithms decide which memory pages to page out, sometimes called swap out, or write
Page_replacement_algorithm
Convex polytope, the n-dimensional analogue of a square and a cube
face lattice of an (n−1)-simplex efficiently, since face lattice enumeration algorithms applicable to general polytopes are more computationally expensive
Hypercube
Parsing algorithm for context-free grammars
Cocke–Younger–Kasami algorithm (alternatively called CYK, or CKY) is a parsing algorithm for context-free grammars published by Itiroo Sakai in 1961. The algorithm is named
CYK_algorithm
Algorithm to compute the maximum flow in a network
Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network. It is sometimes called a "method" instead of an "algorithm" as
Ford–Fulkerson_algorithm
Mathematical problem set on a chessboard
published a highly detailed description of a depth-first backtracking algorithm. The problem of finding all solutions to the 8-queens problem can be quite
Eight_queens_puzzle
Yes-or-no question that cannot ever be solved by a computer
natural numbers. Then we can build an algorithm that enumerates all these statements. This means that there is an algorithm N(n) that, given a natural number
Undecidable_problem
Japanese mathematician (1951-2026)
pivot algorithms, known as the criss-cross method.[FT92][FT97] With David Avis, Fukuda proposed a reverse-search algorithm for the vertex enumeration problem;
Komei_Fukuda
Complexity class
cases. Such a procedure is sometimes called a semi-algorithm, to distinguish it from an algorithm, defined as a complete solution to a decision problem
RE_(complexity)
Sorting algorithm
bogosort (also known as permutation sort and stupid sort) is a sorting algorithm based on the generate and test paradigm. The function successively generates
Bogosort
Class of algorithms that find approximate solutions to optimization problems
techniques to design approximation algorithms. These include the following ones. Greedy algorithm Local search Enumeration and dynamic programming (which
Approximation_algorithm
Problem of finding a cycle through all vertices of a graph
algorithm for finding a Hamiltonian cycle on a directed graph was the enumerative algorithm of Martello. A search procedure by Frank Rubin divides the edges
Hamiltonian_path_problem
Problem-solving technique and algorithmic paradigm
the problem's statement. A brute-force algorithm that finds the divisors of a natural number n would enumerate all integers from 1 to n, and check whether
Brute-force_search
Check the validity of a logic formula
recursively enumerable but not recursive, there exists no general algorithm to solve this problem. Therefore, the Davis–Putnam algorithm only terminates
Davis–Putnam_algorithm
Searching for patterns in text
A string-searching algorithm, sometimes called string-matching algorithm, is an algorithm that searches a body of text for portions that match by pattern
String-searching_algorithm
Geometric shape formed from squares
Polyominoes have been used in popular puzzles since at least 1907, and the enumeration of pentominoes is dated to antiquity. Many results with the pieces made
Polyomino
Study of mathematical groups by means of computers
the Todd–Coxeter algorithm and Knuth–Bendix algorithm for coset enumeration the product-replacement algorithm for finding random elements of a group Two
Computational_group_theory
Ancient algorithm for generating prime numbers
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking
Sieve_of_Eratosthenes
Mathematical function that can be computed by a program
computability theory. Informally, a function is computable if there is an algorithm that computes the value of the function for every value of its argument
Computable_function
Problem in computer science
natural numbers. Then we can build an algorithm that enumerates all these statements. This means that there is an algorithm N(n) that, given a natural number
Halting_problem
Bijective correspondence in mathematics
a nondeterministic algorithm in terms of jeu de taquin. The bijective nature of the correspondence relates it to the enumerative identity ∑ λ ∈ P n (
Robinson–Schensted correspondence
Robinson–Schensted_correspondence
Directed graph with no directed cycles
Bellman–Ford algorithm, pages 588–592, and 24.3, Dijkstra's algorithm, pages 595–601 Page 966 3rd ed., pages 286–307 Skiena, Steven S. (2009), The Algorithm Design
Directed_acyclic_graph
On solvability of Diophantine equations
2}+\cdots +p_{k}^{\,2}=0} . A recursively enumerable set can be characterized as one for which there exists an algorithm that will eventually halt when a member
Hilbert's_tenth_problem
Binary sequence
Intuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free
Algorithmically random sequence
Algorithmically_random_sequence
Trail in a graph that visits each edge once
component of the underlying undirected graph. Fleury's algorithm is an elegant but inefficient algorithm that dates to 1883. Consider a graph known to have
Eulerian_path
Canadian and British computer scientist
Komei Fukuda, Avis proposed a reverse-search algorithm for the vertex enumeration problem; their algorithm generates all of the vertices of a convex polytope
David_Avis
Multi-dimensional generalization of triangle
fact may be used to efficiently enumerate the simplex's face lattice, since more general face lattice enumeration algorithms are more computationally expensive
Simplex
Assembly of written information into a standard order
are not placed in any defined order). A collation algorithm such as the Unicode collation algorithm defines an order through the process of comparing
Collation
Mathematical optimization problem restricted to integers
{\displaystyle V} . In the special case of 0-1 ILP, Lenstra's algorithm is equivalent to complete enumeration: the number of all possible solutions is fixed (2n)
Integer_programming
Data-mining algorithm
Apriori is an algorithm for frequent item set mining and association rule learning over relational databases. It proceeds by identifying the frequent
Apriori_algorithm
Algorithm to calculate the day of the week
Zeller's congruence is an algorithm devised by Christian Zeller in the 19th century to calculate the day of the week for any Julian or Gregorian calendar
Zeller's_congruence
Subpermutation of a longer permutation
characterizing”. A prominent goal in the study of permutation patterns is in the enumeration of permutations avoiding a fixed (and typically short) permutation or
Permutation_pattern
Nash equilibrium of a bimatrix game algorithm
The Lemke–Howson algorithm is an algorithm that computes a Nash equilibrium of a bimatrix game, named after its inventors, Carlton E. Lemke and J. T.
Lemke–Howson_algorithm
Vertices whose removal breaks all cycles
(2008), "On the minimum feedback vertex set problem: exact and enumeration algorithms.", Algorithmica, 52 (2): 293–307, CiteSeerX 10.1.1.722.8913, doi:10
Feedback_vertex_set
Branch of discrete mathematics
concerns the enumeration of combinatorial structures using tools from complex analysis and probability theory. In contrast with enumerative combinatorics
Combinatorics
Partition-based graph traversal method
{\displaystyle \sigma =(v_{1},\dots ,v_{n})} be an enumeration of the vertices of V {\displaystyle V} . The enumeration σ {\displaystyle \sigma } is a LexBFS ordering
Lexicographic breadth-first search
Lexicographic_breadth-first_search
American computer scientist
research concerns the design and analysis of algorithms for random sampling and approximate combinatorial enumeration. Goldberg did her undergraduate studies
Leslie_Ann_Goldberg
Inference algorithm for hidden Markov models
The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables
Forward–backward_algorithm
Use of functions that call themselves
even if this program contains no explicit repetitions. — Niklaus Wirth, Algorithms + Data Structures = Programs, 1976 Most computer programming languages
Recursion_(computer_science)
Optimization technique
designed to find, generate, tune, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem
Metaheuristic
Polish computer scientist (born 1950)
Marek; Jackowski, Bogusław (April 1985). "A generalized implicit enumeration algorithm for graph coloring". Communications of the ACM. 28 (4): 412–418
Bogusław_Jackowski
efficiency A property of an algorithm which relates to the number of computational resources used by the algorithm. An algorithm must be analyzed to determine
Glossary_of_computer_science
Intersection graph for intervals on the real number line
time without using their cliques. The original linear time recognition algorithm of Booth & Lueker (1976) is based on their complex PQ tree data structure
Interval_graph
Method for mathematical optimization
optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general
Criss-cross_algorithm
periodic graph enumeration algorithms, including modifying extant nets to produce new ones, but there appear to be two major classes of enumerators. One of the
Periodic_graph_(geometry)
Suite of IETF specifications
Denial-of-Service Algorithmic Complexity Attacks on DNS Version: January 2024" (PDF). ATHENE. (press release) "NSEC5: Provably Preventing DNSSEC Zone Enumeration". Authenticated
Domain Name System Security Extensions
Domain_Name_System_Security_Extensions
Methodic assignment of colors to elements of a graph
these algorithms are sometimes called sequential coloring algorithms. The maximum (worst) number of colors that can be obtained by the greedy algorithm, by
Graph_coloring
Concept in mathematics
correspondence, also referred to as the RSK correspondence or RSK algorithm, is a combinatorial bijection between matrices A with non-negative integer
Robinson–Schensted–Knuth correspondence
Robinson–Schensted–Knuth_correspondence
Rational number sequence
describes an algorithm for generating Bernoulli numbers with Babbage's machine; it is disputed whether Lovelace or Babbage developed the algorithm. As a result
Bernoulli_number
Framework for analyzing machine learning algorithms
Algorithmic learning theory is a mathematical framework for analyzing machine learning problems and algorithms. Synonyms include formal learning theory
Algorithmic_learning_theory
Convex hull of a finite set of points in a Euclidean space
known as the vertex enumeration problem and the problem of the construction of a H-representation is known as the facet enumeration problem. While the
Convex_polytope
Control flow construct for executing code repeatedly
alternatively, LOOPSTART: do_work() if condition then goto LOOPSTART end if An enumeration (also known as an determinate loop) is a loop intended to iterate over
Loop_(statement)
Process of finding the optimal set of variables for a machine learning algorithm
the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning
Hyperparameter_optimization
Program to compare computer programming languages
The TPK algorithm is a simple program introduced by Donald Knuth and Luis Trabb Pardo to illustrate the evolution of computer programming languages. In
TPK_algorithm
Probabilistic primality test
or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number is likely to be prime, similar
Miller–Rabin_primality_test
Optimization problem in computer science
) in the lattice dimension. The former class of algorithms most notably includes lattice enumeration and random sampling reduction, while the latter includes
Lattice_problem
Set that intersects every one of a family of sets
family of sets has been studied, in particular in the framework of enumeration algorithms. Axiom of choice Permanent John Mackintosh Howie (1995). Fundamentals
Transversal_(combinatorics)
British geometer
the Italian school of algebraic geometry. The Todd–Coxeter algorithm for coset enumeration is a major method of computational algebra, and dates from
J._A._Todd
Decision problem in computer science
programming algorithms that can solve it exactly. As both n and L grow large, SSP is NP-hard. The complexity of the best known algorithms is exponential
Subset_sum_problem
Task of computing complete subgraphs
1137/050643684. Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Algorithm Theory: SWAT 2004 (PDF), Lecture Notes in Computer
Clique_problem
Solution of some Diophantine equation
and only if it is computably enumerable. A set of integers S is computably enumerable if and only if there is an algorithm that, when given an integer
Diophantine_set
Ulfarsson, Henning (2024), "Combinatorial Exploration: An algorithmic framework for enumeration", arXiv:2202.07715 [math.CO]. Albert, Michael H.; Homberger
Enumerations of specific permutation classes
Enumerations_of_specific_permutation_classes
Data mining technique for simultaneous clustering of the rows and columns of a matrix
exhaustive enumeration algorithms such as CCC-Biclustering and e-CCC-Biclustering. The approximate patterns in CCC-Biclustering algorithms allow a given
Biclustering
Algorithm for searching a problem space
computer science and operations research, a memetic algorithm (MA) is an extension of an evolutionary algorithm (EA) that aims to accelerate the evolutionary
Memetic_algorithm
Mathematical puzzle game
(2018-11-14) [2018-08-09, 2017-12, 2017-08-09, 2016-04-22]. "Loopless Gray Code Enumeration and the Tower of Bucharest" (PDF). Theoretical Computer Science. 748
Tower_of_Hanoi
Type of database query
context of enumeration algorithms, with a characterization (under some computational hardness assumptions) of the queries for which enumeration can be performed
Conjunctive_query
Complexity class used to classify decision problems
"nondeterministic, polynomial time". These two definitions are equivalent because the algorithm based on the Turing machine consists of two phases, the first of which
NP_(complexity)
Mathematical term
{Aj}j∈J. An enumeration of a set S gives an index set J ⊂ N {\displaystyle J\subset \mathbb {N} } , where f : J → S is the particular enumeration of S. Any
Index_set
Measure of algorithmic complexity
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is
Kolmogorov_complexity
OV in complexity theory
pairwise dot product algorithm deteriorates. This is due to the bit-parallel and combinatorial techniques used by these algorithms become ineffective as
Orthogonal_vectors_problem
Tree which includes all vertices of a graph
and it is itself). Several pathfinding algorithms, including Dijkstra's algorithm and the A* search algorithm, internally build a spanning tree as an
Spanning_tree
Concept in computability theory
from A to B exists, then every algorithm for B can be used to produce an algorithm for A, by inserting the algorithm for B at each place where the oracle
Turing_reduction
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ENUMERATION ALGORITHM
ENUMERATION ALGORITHM
ENUMERATION ALGORITHM
ENUMERATION ALGORITHM
ENUMERATION ALGORITHM
ENUMERATION ALGORITHM
ENUMERATION ALGORITHM
ENUMERATION ALGORITHM
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