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Transitive closure

In mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets R+ is the unique minimal transitive superset of R.

Products, In logic and computational complexity & In graph theory

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Overview

Transitive relations and examples

Existence and description

Properties

In graph theory

In logic and computational complexity

In database query languages

Algorithms

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Transitive closure

Nodes72
Edges71
Triples156
Avg. degree1.97
Density0.027778
Components1

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Transitive closure

Top relations

related to References · 89
Transitive closure → Abraham Silberschatz, ACM SIGACT-SIGPLAN Symposium, Afrati, Aho, Alfred, Ann, Appendix, Applied, Automata Theory, Benedikt, Boolean, Computer Science, Database System Concepts, Databases, Datalog, Definability, EDBT, Edward, Efficient, Elements
related to In logic and computational complexity · 16
Transitive closure → Alfred Aho, FO, Gaifman-local, In, Jeffrey Ullman, NL, NL-complete, PSPACE, Ronald Fagin, Similarly, STCON, TC, The, This, When, With
related to In database query languages · 14
Transitive closure → BY, Datalog, IBM Db2, Microsoft SQL Server, MySQL, Oracle, Oracle Database, PostgreSQL, RECURSIVEconstruct, Since, SQL, SQLite, START WITHthat, The SQL
related to Algorithms · 11
Transitive closure → DAG, Efficient, Floyd, For, However, Its, Nuutila, Purdom's, Reducing, The, Warshall
related to In graph theory · 6
Transitive closure → After, Boolean, DAG, In, That, The
related to Transitive relations and examples · 6
Transitive closure → Every, Examples, One, Simply, Symbolically, The
related to Existence and description · 5
Transitive closure → For, Furthermore, The, This, To
related to External links · 4
Transitive closure → Repository, Steven Skiena, The Stony Brook Algorithm, Transitive
related to Properties · 3
Transitive closure → The, This, To
is a · 1
Transitive closure → equivalent formulation of the problem of finding the components of the graph

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Important terminology

transitive closure relation set displaystyle graph one theory isbn relations finite smallest logic also model pp binary reduction minimal doi

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Transitive closureis aequivalent formulation of the problem of finding the components of the graph0.90text
Transitive closurerelated to AlgorithmsEfficient0.60section
Transitive closurerelated to AlgorithmsNuutila0.60section
Transitive closurerelated to AlgorithmsReducing0.60section
Transitive closurerelated to AlgorithmsHowever0.60section
Transitive closurerelated to AlgorithmsThe0.60section
Transitive closurerelated to AlgorithmsFloyd0.60section
Transitive closurerelated to AlgorithmsWarshall0.60section
Transitive closurerelated to AlgorithmsFor0.60section
Transitive closurerelated to AlgorithmsPurdom's0.60section
Transitive closurerelated to AlgorithmsDAG0.60section
Transitive closurerelated to AlgorithmsIts0.60section

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