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Enumeration algorithm

In computer science, an enumeration algorithm is an algorithm that enumerates the answers to a computational problem. Formally, such an algorithm applies to problems that take an input and produce a list of solutions, similarly to function problems. For each input, the enumeration algorithm must produce the list of all solutions, without duplicates, and…

Science, Examples of enumeration problems & Common complexity classes

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Examples of enumeration problems

Vertex enumeration problem Polytope System Linear inequalities Vertices

31 related topics

Common complexity classes

Computational complexity theory Complexity classes Polynomial time Decision problem Witnesses

8 related topics

Common techniques

Backtracking Partitioning Self-reducible Union Sorted order

7 related topics

Connection to computability theory

Computability theory RE Recursively enumerable

3 related topics

Topics to explore

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Overview

Computer science
Algorithm
Enumerates Enumeration
Computational problem
Function problems
Output-sensitive algorithms Output-sensitive algorithm

Formal definitions

Strings String (computer science)
Alphabet Alphabet (computer science)

Common complexity classes

Computational complexity theory
Complexity classes Complexity class
Polynomial time
Decision problem
Witnesses Witness (mathematics)
Class Class (complexity theory)
NP NP (complexity)
Polynomial delay

Common techniques

Backtracking
Partitioning Partition (mathematics)
Self-reducible
Union Union (set theory)
Sorted order Sorting
Hash table
Cartesian product

Examples of enumeration problems

Vertex enumeration problem
Polytope
System System of equations
Linear inequalities Linear inequality
Vertices Vertex (geometry)
Minimal transversals Minimal transversal?action=edit&redlink=1
Hypergraph Hypergraph (mathematics)
Monotone dualization
Database theory
Graph theory
Database query
Conjunctive query
Monadic second-order
Linear Linear time
Constant Constant time
Enumerating maximal cliques Clique problem
Bron–Kerbosch algorithm
Matroids Matroid
Greedoids Greedoid
Independent sets Independent set (graph theory)
Paths Path (graph theory)
Cuts Cut (graph theory)
Satisfying assignments Boolean satisfiability problem
Boolean functions Boolean function
Conjunctive normal form
Disjunctive normal form
Binary decision diagram
OBDD
Boolean circuit
Knowledge compilation

Connection to computability theory

Advanced semantic analysis

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Map overview Semantic statistics

Enumeration algorithm

Nodes64

Edges63

Triples17

Avg. degree1.97

Density0.03125

Components1

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Enumeration algorithm

Top relations

related to Connection to computability theory · 3

Enumeration algorithm → RE, The, This

is a · 1

Enumeration algorithm → algorithm that enumerates the answers to a computational problem

Important terminology Word statistics

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Important terminology

algorithm input problems enumeration class problem time output solutions polynomial delay enumerating produce sets two classes theory complexity must preprocessing

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Enumeration algorithm	is a	algorithm that enumerates the answers to a computational problem	0.90	text
matroids	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
greedoidsSeveral problems on graphs	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
e.g.	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
enumerating independent sets	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
paths	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
cuts	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
etc.Enumerating the satisfying assignments of representations of Boolean functions	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
a Boolean formula written in conjunctive normal form or disjunctive normal form	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
a binary decision diagram such as an OBDD	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
or a Boolean circuit in restricted classes studied in knowledge compilation	instance of	Kerbosch algorithmListing all elements of structures	0.80	text
NNF	instance of	Kerbosch algorithmListing all elements of structures	0.80	text

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