@prefix dbo:	<http://dbpedia.org/ontology/> .
@prefix dbr:	<http://dbpedia.org/resource/> .
dbr:Graph_theory	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Shortest_path_problem	dbo:wikiPageWikiLink	dbr:Topological_sorting .
<http://dbpedia.org/resource/Make_(software)>	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Weak_component	dbo:wikiPageWikiLink	dbr:Topological_sorting .
<http://dbpedia.org/resource/Coffman\u2013Graham_algorithm>	dbo:wikiPageWikiLink	dbr:Topological_sorting .
<http://dbpedia.org/resource/Tarjan\u0027s_strongly_connected_components_algorithm>	dbo:wikiPageWikiLink	dbr:Topological_sorting .
<http://dbpedia.org/resource/Push\u2013relabel_maximum_flow_algorithm>	dbo:wikiPageWikiLink	dbr:Topological_sorting .
<http://dbpedia.org/resource/APT_(software)>	dbo:wikiPageWikiLink	dbr:Topological_sorting .
@prefix foaf:	<http://xmlns.com/foaf/0.1/> .
@prefix wikipedia-en:	<http://en.wikipedia.org/wiki/> .
wikipedia-en:Topological_sorting	foaf:primaryTopic	dbr:Topological_sorting .
dbr:Glossary_of_graph_theory	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:List_of_graph_theory_topics	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Acyclic_orientation	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Partially_ordered_set	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Directed_graph	dbo:wikiPageWikiLink	dbr:Topological_sorting .
<http://dbpedia.org/resource/Cycle_(graph_theory)>	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Data_lineage	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Dependency_graph	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Depth-first_search	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:C3_linearization	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Directed_acyclic_graph	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Linear_extension	dbo:wikiPageWikiLink	dbr:Topological_sorting .
@prefix rdf:	<http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix yago:	<http://dbpedia.org/class/yago/> .
dbr:Topological_sorting	rdf:type	yago:Procedure101023820 ,
		yago:YagoPermanentlyLocatedEntity ,
		yago:Rule105846932 ,
		yago:SortingAlgorithm105847658 ,
		yago:WikicatSortingAlgorithms ,
		yago:Algorithm105847438 .
@prefix owl:	<http://www.w3.org/2002/07/owl#> .
dbr:Topological_sorting	rdf:type	owl:Thing ,
		yago:VisualCommunication106873252 ,
		yago:Act100030358 ,
		yago:PsychologicalFeature100023100 ,
		yago:Activity100407535 ,
		yago:WikicatGraphAlgorithms ,
		yago:Communication100033020 ,
		yago:Abstraction100002137 ,
		yago:Event100029378 ,
		yago:WikicatDirectedGraphs ,
		yago:Graph107000195 .
@prefix rdfs:	<http://www.w3.org/2000/01/rdf-schema#> .
dbr:Topological_sorting	rdfs:label	"\u0422\u043E\u043F\u043E\u043B\u043E\u0433\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0441\u043E\u0440\u0442\u0438\u0440\u043E\u0432\u043A\u0430"@ru ,
		"\u0422\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0435 \u0441\u043E\u0440\u0442\u0443\u0432\u0430\u043D\u043D\u044F"@uk ,
		"Ordenamiento topol\u00F3gico"@es ,
		"\uC704\uC0C1\uC815\uB82C"@ko ,
		"Ordinamento topologico"@it ,
		"\u62D3\u64B2\u6392\u5E8F"@zh ,
		"Ordena\u00E7\u00E3o topol\u00F3gica"@pt ,
		"Sortowanie topologiczne"@pl ,
		"Tri topologique"@fr ,
		"Topologische Sortierung"@de ,
		"\u03A4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AE \u03C4\u03B1\u03BE\u03B9\u03BD\u03CC\u03BC\u03B7\u03C3\u03B7"@el ,
		"Topological sorting"@en ,
		"\u30C8\u30DD\u30ED\u30B8\u30AB\u30EB\u30BD\u30FC\u30C8"@ja ;
	rdfs:comment	"\uC704\uC0C1 \uC815\uB82C(topological sorting)\uC740 \uC720\uD5A5 \uADF8\uB798\uD504\uC758 \uAF2D\uC9D3\uC810\uB4E4(vertex)\uC744 \uBCC0\uC758 \uBC29\uD5A5\uC744 \uAC70\uC2A4\uB974\uC9C0 \uC54A\uB3C4\uB85D \uB098\uC5F4\uD558\uB294 \uAC83\uC744 \uC758\uBBF8\uD55C\uB2E4. \uC704\uC0C1\uC815\uB82C\uC744 \uAC00\uC7A5 \uC798 \uC124\uBA85\uD574 \uC904 \uC218 \uC788\uB294 \uC608\uB85C \uB300\uD559\uC758 \uC120\uC218\uACFC\uBAA9(prerequisite) \uAD6C\uC870\uB97C \uC608\uB85C \uB4E4 \uC218 \uC788\uB2E4. \uB9CC\uC57D \uD2B9\uC815 \uC218\uAC15\uACFC\uBAA9\uC5D0 \uC120\uC218\uACFC\uBAA9\uC774 \uC788\uB2E4\uBA74 \uADF8 \uC120\uC218 \uACFC\uBAA9\uBD80\uD130 \uC218\uAC15\uD574\uC57C \uD558\uBBC0\uB85C, \uD2B9\uC815 \uACFC\uBAA9\uB4E4\uC744 \uC218\uAC15\uD574\uC57C \uD560 \uB54C \uC704\uC0C1 \uC815\uB82C\uC744 \uD1B5\uD574 \uC62C\uBC14\uB978 \uC218\uAC15 \uC21C\uC11C\uB97C \uCC3E\uC544\uB0BC \uC218 \uC788\uB2E4. \uC774\uC640 \uAC19\uC774 \uC120\uD6C4 \uAD00\uACC4\uAC00 \uC815\uC758\uB41C \uC0C1\uC5D0\uC11C \uC120\uD6C4 \uAD00\uACC4\uC5D0 \uB530\uB77C \uC815\uB82C\uD558\uAE30 \uC704\uD574 \uC704\uC0C1 \uC815\uB82C\uC744 \uC774\uC6A9\uD560 \uC218 \uC788\uB2E4. \uC815\uB82C\uC758 \uC21C\uC11C\uB294 \uC720\uD5A5 \uADF8\uB798\uD504\uC758 \uAD6C\uC870\uC5D0 \uB530\uB77C \uC5EC\uB7EC \uAC1C\uC758 \uC885\uB958\uAC00 \uB098\uC62C \uC218 \uC788\uB2E4. \uC704\uC0C1 \uC815\uB82C\uC774 \uC131\uB9BD\uD558\uAE30 \uC704\uD574\uC11C\uB294 \uBC18\uB4DC\uC2DC \uADF8\uB798\uD504\uC758 \uC21C\uD658\uC774 \uC874\uC7AC\uD558\uC9C0 \uC54A\uC544\uC57C \uD55C\uB2E4. \uC989, \uADF8\uB798\uD504\uAC00 \uBE44\uC21C\uD658 \uC720\uD5A5 \uADF8\uB798\uD504(directed acyclic graph)\uC5EC\uC57C \uD55C\uB2E4."@ko ,
		"Una ordenaci\u00F3n topol\u00F3gica (topological sort, topological ordering, topsort o toposort en ingl\u00E9s) de un grafo ac\u00EDclico dirigido G es una ordenaci\u00F3n lineal de todos los nodos de G que satisface que si G contiene la arista dirigida uv entonces el nodo u aparece antes del nodo v. La condici\u00F3n que el grafo no contenga ciclos es importante, ya que no se puede obtener ordenaci\u00F3n topol\u00F3gica de grafos que contengan ciclos. Para poder encontrar la ordenaci\u00F3n topol\u00F3gica del grafo G deberemos aplicar una modificaci\u00F3n del algoritmo de b\u00FAsqueda en profundidad (DFS)."@es ,
		"En th\u00E9orie des graphes, et plus sp\u00E9cialement en algorithmique des graphes, un tri topologique d'un graphe acyclique orient\u00E9 (ou dag, de l'anglais directed acyclic graph) est un ordre total sur l'ensemble des sommets, dans lequel s pr\u00E9c\u00E8de t pour tout arc d'un sommet s \u00E0 un sommet t. En d'autres termes, un tri topologique est une extension lin\u00E9aire de l'ordre partiel sur les sommets d\u00E9termin\u00E9s par les arcs."@fr ,
		"In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. Precisely, a topological sort is a graph traversal in which each node v is visited only after all its dependencies are visited. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are know"@en ,
		"Topologische Sortierung bezeichnet in der Mathematik eine Reihenfolge von Dingen, bei der vorgegebene Abh\u00E4ngigkeiten erf\u00FCllt sind. Anstehende T\u00E4tigkeiten einer Person etwa unterliegen einer Halbordnung: es existieren Bedingungen wie \u201ET\u00E4tigkeit A muss vor T\u00E4tigkeit B erledigt werden\u201C. Eine Reihenfolge, welche alle Bedingungen erf\u00FCllt, nennt man topologische Sortierung der Menge anstehender T\u00E4tigkeiten. Im Gegensatz zur Sortierung einer Totalordnung ist die Reihenfolge nicht eindeutig, sondern es kann mehrere M\u00F6glichkeiten geben. Wenn gegenseitige Abh\u00E4ngigkeiten bestehen, ist eine topologische Sortierung unm\u00F6glich."@de ,
		"In teoria dei grafi un ordinamento topologico (in inglese topological sort) \u00E8 un ordinamento lineare di tutti i vertici di un grafo diretto. I nodi di un grafo si definiscono ordinati topologicamente se i nodi sono disposti in modo tale che ogni nodo viene prima di tutti i nodi collegati ai suoi archi uscenti.L'ordinamento topologico non \u00E8 un ordinamento totale, poich\u00E9 la soluzione pu\u00F2 non essere unica. Nel caso peggiore infatti si possono avere ordinamenti topologici diversi che corrispondono a tutte le possibili permutazioni degli nodi. \u00C8 possibile ordinare topologicamente un grafo se e solo se non contiene cicli (cio\u00E8 solo se \u00E8 un grafo aciclico diretto), e sono noti algoritmi per determinare un ordinamento topologico in tempo lineare."@it ,
		"Em teoria dos grafos, uma ordena\u00E7\u00E3o topol\u00F3gica de um digrafo ac\u00EDclico (DAG) \u00E9 uma ordem linear de seus n\u00F3s em que cada n\u00F3 vem antes de todos n\u00F3s para os quais este tenha arestas de sa\u00EDda. Cada DAG tem uma ou mais ordena\u00E7\u00F5es topol\u00F3gicas. Mais formalmente, define-se a rela\u00E7\u00E3o acessibilidade R sobre os n\u00F3s do DAG tal que xRy se e somente se existe um caminho dirigido de x para y. Ent\u00E3o, R \u00E9 uma ordem parcial, e uma ordena\u00E7\u00E3o topol\u00F3gica \u00E9 uma desta ordem parcial, isto \u00E9, uma ordem total compat\u00EDvel com a ordem parcial."@pt ,
		"\u5728\u8BA1\u7B97\u673A\u79D1\u5B66\u9886\u57DF\uFF0C\u6709\u5411\u56FE\u7684\u62D3\u6251\u6392\u5E8F\u6216\u62D3\u64B2\u5B9A\u5E8F\u662F\u5BF9\u5176\u9876\u70B9\u7684\u4E00\u79CD\u7EBF\u6027\u6392\u5E8F\uFF0C\u4F7F\u5F97\u5BF9\u4E8E\u4ECE\u9876\u70B9\u5230\u9876\u70B9\u7684\u6BCF\u4E2A\u6709\u5411\u8FB9\uFF0C\u5728\u6392\u5E8F\u4E2D\u90FD\u5728\u4E4B\u524D\u3002 \u4F8B\u5982\uFF0C\u56FE\u5F62\u7684\u9876\u70B9\u53EF\u4EE5\u8868\u793A\u8981\u6267\u884C\u7684\u4EFB\u52A1\uFF0C\u5E76\u4E14\u8FB9\u53EF\u4EE5\u8868\u793A\u4E00\u4E2A\u4EFB\u52A1\u5FC5\u987B\u5728\u53E6\u4E00\u4E2A\u4EFB\u52A1\u4E4B\u524D\u6267\u884C\u7684\u7EA6\u675F\uFF1B\u5728\u8FD9\u4E2A\u5E94\u7528\u4E2D\uFF0C\u62D3\u6251\u6392\u5E8F\u53EA\u662F\u4E00\u4E2A\u6709\u6548\u7684\u4EFB\u52A1\u987A\u5E8F\u3002 \u5F53\u4E14\u4EC5\u5F53\u56FE\u4E2D\u6CA1\u6709\u5B9A\u5411\u73AF\u65F6\uFF08\u5373\u6709\u5411\u65E0\u73AF\u56FE\uFF09\uFF0C\u624D\u6709\u53EF\u80FD\u8FDB\u884C\u62D3\u6251\u6392\u5E8F\u3002 \u4EFB\u4F55\u6709\u5411\u65E0\u73AF\u56FE\u81F3\u5C11\u6709\u4E00\u4E2A\u62D3\u6251\u6392\u5E8F\u3002\u5DF2\u77E5\u6709\u7B97\u6CD5\u53EF\u4EE5\u5728\u7EBF\u6027\u65F6\u95F4\u5185\uFF0C\u6784\u5EFA\u4EFB\u4F55\u6709\u5411\u65E0\u73AF\u56FE\u7684\u62D3\u6251\u6392\u5E8F\u3002 \u5728\u56FE\u8BBA\u4E2D\uFF0C\u7531\u4E00\u4E2A\u6709\u5411\u65E0\u73AF\u56FE\u7684\u9876\u70B9\u7EC4\u6210\u7684\u5E8F\u5217\uFF0C\u5F53\u4E14\u4EC5\u5F53\u6EE1\u8DB3\u4E0B\u5217\u6761\u4EF6\u65F6\uFF0C\u624D\u80FD\u79F0\u4E3A\u8BE5\u56FE\u7684\u4E00\u4E2A\u62D3\u6251\u6392\u5E8F\uFF08\u82F1\u8A9E\uFF1ATopological sorting\uFF09\uFF1A 1. \n* \u5E8F\u5217\u4E2D\u5305\u542B\u6BCF\u4E2A\u9876\u70B9\uFF0C\u4E14\u6BCF\u4E2A\u9876\u70B9\u53EA\u51FA\u73B0\u4E00\u6B21\uFF1B 2. \n* \u82E5A\u5728\u5E8F\u5217\u4E2D\u6392\u5728B\u7684\u524D\u9762\uFF0C\u5219\u5728\u56FE\u4E2D\u4E0D\u5B58\u5728\u4ECEB\u5230A\u7684\u8DEF\u5F84\u3002"@zh ,
		"\u03A4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AE \u03C4\u03B1\u03BE\u03B9\u03BD\u03CC\u03BC\u03B7\u03C3\u03B7 \u03AE \u03B1\u03BB\u03BB\u03B9\u03CE\u03C2 \u03C4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AE \u03B4\u03B9\u03AC\u03C4\u03B1\u03BE\u03B7 (\u03B1\u03B3\u03B3\u03BB\u03B9\u03BA\u03AC: Topological sorting) \u03B5\u03BD\u03CC\u03C2 \u039A\u03B1\u03C4\u03B5\u03C5\u03B8\u03C5\u03BD\u03CC\u03BC\u03B5\u03BD\u03BF\u03C5 \u0386\u03BA\u03C5\u03BA\u03BB\u03BF\u03C5 \u0393\u03C1\u03AC\u03C6\u03BF\u03C5 (Directed Acyclic Graph \u03AE DAG), \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03C3\u03C4\u03B7 \u0398\u03B5\u03C9\u03C1\u03AF\u03B1 \u0393\u03C1\u03AC\u03C6\u03C9\u03BD \u03B7 \u03B3\u03C1\u03B1\u03BC\u03BC\u03B9\u03BA\u03AE \u03B4\u03B9\u03AC\u03C4\u03B1\u03BE\u03B7 \u03C4\u03C9\u03BD \u03BA\u03CC\u03BC\u03B2\u03C9\u03BD, \u03AD\u03C4\u03C3\u03B9 \u03CE\u03C3\u03C4\u03B5 \u03BA\u03AC\u03B8\u03B5 \u03C0\u03C1\u03CC\u03B3\u03BF\u03BD\u03BF\u03C2 \u03B5\u03BD\u03CC\u03C2 v \u03C0\u03C1\u03BF\u03B7\u03B3\u03B5\u03AF\u03C4\u03B1\u03B9 \u03C4\u03BF\u03C5 v \u03C3\u03C4\u03B7 \u03B4\u03B9\u03AC\u03C4\u03B1\u03BE\u03B7. \u039A\u03AC\u03B8\u03B5 \u039A\u03B1\u03C4\u03B5\u03C5\u03B8\u03C5\u03BD\u03CC\u03BC\u03B5\u03BD\u03BF\u03C2 \u0386\u03BA\u03C5\u03BA\u03BB\u03BF\u03C2 \u0393\u03C1\u03AC\u03C6\u03BF\u03C2 \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03AD\u03C7\u03B5\u03B9 \u03BC\u03AF\u03B1 \u03AE \u03C0\u03B5\u03C1\u03B9\u03C3\u03C3\u03CC\u03C4\u03B5\u03C1\u03B5\u03C2 \u03C4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AD\u03C2 \u03B4\u03B9\u03B1\u03C4\u03AC\u03BE\u03B5\u03B9\u03C2."@el ,
		"\u30C8\u30DD\u30ED\u30B8\u30AB\u30EB\u30BD\u30FC\u30C8\uFF08\u82F1: topological sort\uFF09\u306F\u3001\u30B0\u30E9\u30D5\u7406\u8AD6\u306B\u304A\u3044\u3066\u3001\u6709\u5411\u975E\u5DE1\u56DE\u30B0\u30E9\u30D5\uFF08\u82F1: directed acyclic graph, DAG\uFF09\u306E\u5404\u30CE\u30FC\u30C9\u3092\u9806\u5E8F\u4ED8\u3051\u3057\u3066\u3001\u3069\u306E\u30CE\u30FC\u30C9\u3082\u305D\u306E\u51FA\u529B\u8FBA\u306E\u5148\u306E\u30CE\u30FC\u30C9\u3088\u308A\u524D\u306B\u304F\u308B\u3088\u3046\u306B\u4E26\u3079\u308B\u3053\u3068\u3067\u3042\u308B\u3002\u6709\u5411\u975E\u5DE1\u56DE\u30B0\u30E9\u30D5\u306F\u5FC5\u305A\u30C8\u30DD\u30ED\u30B8\u30AB\u30EB\u30BD\u30FC\u30C8\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u6709\u5411\u975E\u5DE1\u56DE\u30B0\u30E9\u30D5\u306E\u30CE\u30FC\u30C9\u306E\u96C6\u5408\u306B\u5230\u9054\u53EF\u80FD\u6027\u95A2\u4FC2 R (\u30CE\u30FC\u30C9 x \u304B\u3089 y \u3078\u306E(\u5404\u8FBA\u306E\u5411\u304D\u306B\u9006\u884C\u3057\u306A\u3044)\u7D4C\u8DEF\u304C\u5B58\u5728\u3059\u308B\u3068\u304D\u3001\u307E\u305F\u305D\u306E\u3068\u304D\u306B\u9650\u308A xRy \u3068\u3059\u308B)\u3092\u5B9A\u3081\u308B\u3068\u3001R \u306F\u534A\u9806\u5E8F\u95A2\u4FC2\u3068\u306A\u308B\u3002\u30C8\u30DD\u30ED\u30B8\u30AB\u30EB\u30BD\u30FC\u30C8\u3068\u306F\u3001\u3053\u306E R \u3092\u5168\u9806\u5E8F\u306B\u306A\u308B\u3088\u3046\u306B\u62E1\u5F35\u3057\u305F\u3082\u306E\u3068\u307F\u306A\u305B\u308B\u3002"@ja ,
		"Sortowanie topologiczne skierowanego grafu acyklicznego \u2013 liniowe uporz\u0105dkowanie wierzcho\u0142k\u00F3w, w kt\u00F3rym je\u015Bli istnieje kraw\u0119d\u017A skierowana prowadz\u0105ca od wierzcho\u0142ka do to znajdzie si\u0119 przed wierzcho\u0142kiem Innymi s\u0142owy, ka\u017Cdy wierzcho\u0142ek poprzedza wszystkie te wierzcho\u0142ki, do kt\u00F3rych prowadz\u0105 wychodz\u0105ce od niego kraw\u0119dzie. Wierzcho\u0142ki w ka\u017Cdym grafie acyklicznym skierowanym mo\u017Cna posortowa\u0107 topologicznie na jeden lub wi\u0119cej sposob\u00F3w."@pl ,
		"\u0422\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0435 \u0441\u043E\u0440\u0442\u0443\u0432\u0430\u043D\u043D\u044F \u2014 \u0432\u043F\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u0443\u0432\u0430\u043D\u043D\u044F \u0432\u0435\u0440\u0448\u0438\u043D \u0431\u0435\u0437\u043A\u043E\u043D\u0442\u0443\u0440\u043D\u043E\u0433\u043E \u043E\u0440\u0456\u0454\u043D\u0442\u043E\u0432\u0430\u043D\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0443 \u0437\u0433\u0456\u0434\u043D\u043E \u0437 \u0447\u0430\u0441\u0442\u043A\u043E\u0432\u0438\u043C \u043F\u043E\u0440\u044F\u0434\u043A\u043E\u043C, \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u0438\u043C \u0440\u0435\u0431\u0440\u0430\u043C\u0438 \u0446\u044C\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0443 \u043D\u0430 \u043C\u043D\u043E\u0436\u0438\u043D\u0456 \u0439\u043E\u0433\u043E \u0432\u0435\u0440\u0448\u0438\u043D."@uk ,
		"\u0422\u043E\u043F\u043E\u043B\u043E\u0433\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0441\u043E\u0440\u0442\u0438\u0440\u043E\u0432\u043A\u0430 \u2014 \u0443\u043F\u043E\u0440\u044F\u0434\u043E\u0447\u0438\u0432\u0430\u043D\u0438\u0435 \u0432\u0435\u0440\u0448\u0438\u043D \u0431\u0435\u0441\u043A\u043E\u043D\u0442\u0443\u0440\u043D\u043E\u0433\u043E \u043E\u0440\u0438\u0435\u043D\u0442\u0438\u0440\u043E\u0432\u0430\u043D\u043D\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0430 \u0441\u043E\u0433\u043B\u0430\u0441\u043D\u043E \u0447\u0430\u0441\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u043F\u043E\u0440\u044F\u0434\u043A\u0443, \u0437\u0430\u0434\u0430\u043D\u043D\u043E\u043C\u0443 \u0440\u0435\u0431\u0440\u0430\u043C\u0438 \u043E\u0440\u0433\u0440\u0430\u0444\u0430 \u043D\u0430 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0435 \u0435\u0433\u043E \u0432\u0435\u0440\u0448\u0438\u043D."@ru ;
	owl:differentFrom	<http://dbpedia.org/resource/Kuhn\u0027s_algorithm> ;
	foaf:depiction	<http://commons.wikimedia.org/wiki/Special:FilePath/Directed_acyclic_graph_2.svg> ,
		<http://commons.wikimedia.org/wiki/Special:FilePath/Parallel_Topological_Sorting.gif> .
@prefix dct:	<http://purl.org/dc/terms/> .
@prefix dbc:	<http://dbpedia.org/resource/Category:> .
dbr:Topological_sorting	dct:subject	dbc:Articles_with_example_pseudocode ,
		dbc:Graph_algorithms ,
		dbc:Directed_acyclic_graphs ,
		dbc:Sorting_algorithms ;
	dbo:abstract	"Em teoria dos grafos, uma ordena\u00E7\u00E3o topol\u00F3gica de um digrafo ac\u00EDclico (DAG) \u00E9 uma ordem linear de seus n\u00F3s em que cada n\u00F3 vem antes de todos n\u00F3s para os quais este tenha arestas de sa\u00EDda. Cada DAG tem uma ou mais ordena\u00E7\u00F5es topol\u00F3gicas. Mais formalmente, define-se a rela\u00E7\u00E3o acessibilidade R sobre os n\u00F3s do DAG tal que xRy se e somente se existe um caminho dirigido de x para y. Ent\u00E3o, R \u00E9 uma ordem parcial, e uma ordena\u00E7\u00E3o topol\u00F3gica \u00E9 uma desta ordem parcial, isto \u00E9, uma ordem total compat\u00EDvel com a ordem parcial."@pt ,
		"Sortowanie topologiczne skierowanego grafu acyklicznego \u2013 liniowe uporz\u0105dkowanie wierzcho\u0142k\u00F3w, w kt\u00F3rym je\u015Bli istnieje kraw\u0119d\u017A skierowana prowadz\u0105ca od wierzcho\u0142ka do to znajdzie si\u0119 przed wierzcho\u0142kiem Innymi s\u0142owy, ka\u017Cdy wierzcho\u0142ek poprzedza wszystkie te wierzcho\u0142ki, do kt\u00F3rych prowadz\u0105 wychodz\u0105ce od niego kraw\u0119dzie. Wierzcho\u0142ki w ka\u017Cdym grafie acyklicznym skierowanym mo\u017Cna posortowa\u0107 topologicznie na jeden lub wi\u0119cej sposob\u00F3w."@pl ,
		"In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. Precisely, a topological sort is a graph traversal in which each node v is visited only after all its dependencies are visited. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time. Topological sorting has many applications especially in ranking problems such as feedback arc set. Topological sorting is possible even when the DAG has disconnected components."@en ,
		"\uC704\uC0C1 \uC815\uB82C(topological sorting)\uC740 \uC720\uD5A5 \uADF8\uB798\uD504\uC758 \uAF2D\uC9D3\uC810\uB4E4(vertex)\uC744 \uBCC0\uC758 \uBC29\uD5A5\uC744 \uAC70\uC2A4\uB974\uC9C0 \uC54A\uB3C4\uB85D \uB098\uC5F4\uD558\uB294 \uAC83\uC744 \uC758\uBBF8\uD55C\uB2E4. \uC704\uC0C1\uC815\uB82C\uC744 \uAC00\uC7A5 \uC798 \uC124\uBA85\uD574 \uC904 \uC218 \uC788\uB294 \uC608\uB85C \uB300\uD559\uC758 \uC120\uC218\uACFC\uBAA9(prerequisite) \uAD6C\uC870\uB97C \uC608\uB85C \uB4E4 \uC218 \uC788\uB2E4. \uB9CC\uC57D \uD2B9\uC815 \uC218\uAC15\uACFC\uBAA9\uC5D0 \uC120\uC218\uACFC\uBAA9\uC774 \uC788\uB2E4\uBA74 \uADF8 \uC120\uC218 \uACFC\uBAA9\uBD80\uD130 \uC218\uAC15\uD574\uC57C \uD558\uBBC0\uB85C, \uD2B9\uC815 \uACFC\uBAA9\uB4E4\uC744 \uC218\uAC15\uD574\uC57C \uD560 \uB54C \uC704\uC0C1 \uC815\uB82C\uC744 \uD1B5\uD574 \uC62C\uBC14\uB978 \uC218\uAC15 \uC21C\uC11C\uB97C \uCC3E\uC544\uB0BC \uC218 \uC788\uB2E4. \uC774\uC640 \uAC19\uC774 \uC120\uD6C4 \uAD00\uACC4\uAC00 \uC815\uC758\uB41C \uC0C1\uC5D0\uC11C \uC120\uD6C4 \uAD00\uACC4\uC5D0 \uB530\uB77C \uC815\uB82C\uD558\uAE30 \uC704\uD574 \uC704\uC0C1 \uC815\uB82C\uC744 \uC774\uC6A9\uD560 \uC218 \uC788\uB2E4. \uC815\uB82C\uC758 \uC21C\uC11C\uB294 \uC720\uD5A5 \uADF8\uB798\uD504\uC758 \uAD6C\uC870\uC5D0 \uB530\uB77C \uC5EC\uB7EC \uAC1C\uC758 \uC885\uB958\uAC00 \uB098\uC62C \uC218 \uC788\uB2E4. \uC704\uC0C1 \uC815\uB82C\uC774 \uC131\uB9BD\uD558\uAE30 \uC704\uD574\uC11C\uB294 \uBC18\uB4DC\uC2DC \uADF8\uB798\uD504\uC758 \uC21C\uD658\uC774 \uC874\uC7AC\uD558\uC9C0 \uC54A\uC544\uC57C \uD55C\uB2E4. \uC989, \uADF8\uB798\uD504\uAC00 \uBE44\uC21C\uD658 \uC720\uD5A5 \uADF8\uB798\uD504(directed acyclic graph)\uC5EC\uC57C \uD55C\uB2E4. \uC77C\uBC18\uC801\uC778 \uC704\uC0C1 \uC815\uB82C\uC758 \uC801\uC6A9\uC740 \uC8FC\uB85C \uC5C5\uBB34\uC758 \uC77C\uC815\uC744 \uC77C\uC5B4\uB098\uC57C \uD560 \uC21C\uC11C\uC5D0 \uB530\uB77C \uBC30\uCE58\uD558\uAE30 \uC704\uD558\uB294 \uAC83\uC73C\uB85C, \uC774 \uC54C\uACE0\uB9AC\uC998\uC740 \uD504\uB85C\uC81D\uD2B8 \uAD00\uB9AC \uAE30\uBC95\uC744 \uD3C9\uAC00 \uBC0F \uBD84\uC11D\uD558\uAE30 \uC704\uD55C \uAE30\uBC95(PERT)\uC5D0 \uC801\uC6A9\uD558\uAE30 \uC704\uD55C \uBAA9\uC801\uC744 \uC704\uD574 1960\uB144\uB300 \uCD08\uBC18\uBD80\uD130 \uC5F0\uAD6C\uB418\uC5C8\uB2E4 (Jarnagin 1960). \uC774 \uB54C, \uD574\uB2F9 \uC5C5\uBB34\uB294 \uAF2D\uC9D3\uC810\uC73C\uB85C \uD45C\uD604\uB418\uC5C8\uACE0, \uAC01 \uAF2D\uC9D3\uC810\uC744 \uC5F0\uACB0\uD558\uB294 \uBCC0\uC740 \uD574\uB2F9 \uC5C5\uBB34 \uAC04\uC758 \uC120\uD6C4 \uAD00\uACC4\uB97C \uD45C\uD604\uD558\uC600\uB2E4. \uAC00\uB839, \uC637\uC744 \uB2E4\uB9AC\uAE30 \uC704\uD55C \uC5C5\uBB34\uB294 \uBC18\uB4DC\uC2DC \uC637\uC744 \uC138\uD0C1\uAE30\uC5D0 \uB3CC\uB9AC\uB294 \uC5C5\uBB34 \uB4A4\uC5D0 \uBC30\uCE58\uB418\uC5B4\uC57C \uD55C\uB2E4. \uC774\uC640 \uAC19\uC774, \uC704\uC0C1\uC815\uB82C\uC740 \uAC01 \uC5C5\uBB34\uB97C \uC218\uD589\uD558\uAE30 \uC704\uD55C \uC21C\uC11C\uB97C \uC81C\uACF5\uD558\uC600\uB2E4. Topological sorting(\uC704\uC0C1 \uC815\uB82C)\uC740 \uCEF4\uD4E8\uD130 \uACFC\uD559\uC5D0\uC11C, \uBC29\uD5A5 \uADF8\uB798\uD504\uC758 \uC704\uC0C1 \uC815\uB82C \uB610\uB294 \uC704\uC0C1 \uBC30\uCE58\uB294 \uC815\uC810\uC758 \uC120\uD615 \uC21C\uC11C\uC774\uB2E4. \uAF2D\uC9D3\uC810 u\uC5D0\uC11C \uAF2D\uC9D3\uC810 v\uB85C\uC758 \uBAA8\uB4E0 \uBC29\uD5A5 \uAF2D\uC9D3\uC810 uv\uB294 v\uC758 \uC21C\uC11C \uC804\uC5D0 u\uAC00 \uC624\uB294 \uAC83\uC774\uB2E4. \uC608\uB97C \uB4E4\uC5B4, \uADF8\uB798\uD504\uC758 \uAF2D\uC9D3\uC810\uC740 \uC544\uB9C8 \uC218\uD589\uD558\uB294 \uC77C\uC740 \uB300\uD45C\uD55C\uB2E4. \uADF8\uB9AC\uACE0 \uAF2D\uC9D3\uC810\uC740 \uC5B4\uB5A4 \uC77C\uC774 \uB2E4\uB978 \uAC83\uBCF4\uB2E4 \uBA3C\uC800 \uC218\uD589\uB418\uC5B4\uC57C \uD558\uB294 \uD5C8\uAC00\uB418\uC9C0 \uC54A\uC740 \uAC83\uC744 \uB300\uD45C\uD55C\uB2E4. \uC774\uB7EC\uD55C \uAC83\uC5D0\uC11C, \uC704\uC0C1 \uBC30\uC5F4\uC740 \uC77C\uC758 \uC720\uC6A9\uD55C \uC21C\uC11C\uC5D0 \uBD88\uACFC\uD558\uB2E4. \uC815\uD655\uD788 \uC704\uC0C1 \uC815\uB82C\uC740 \uBAA8\uB4E0 \uC885\uC18D\uC131\uC744 \uBC29\uBB38\uD55C \uD6C4\uC5D0\uB9CC \uAC01 \uB178\uB4DC v\uB97C \uBC29\uBB38\uD558\uB294 \uADF8\uB798\uD504 \uC21C\uD658\uC774\uB2E4. \uC704\uC0C1 \uBC30\uC5F4\uC740 \uAC00\uB2A5\uD558\uB2E4. \uC815\uB9D0 \uB9CC\uC57D\uC5D0 \uADF8\uB798\uD504 \uBC29\uD5A5\uC774 \uC5C6\uB294 \uC21C\uD658\uC774\uB77C\uBA74, \uC544\uB9C8 \uADF8\uAC83\uC740 \uBC29\uD5A5 \uC21C\uD658 \uADF8\uB798\uD504(DAG)\uC77C \uAC83\uC774\uB2E4. \uC5B4\uB5A4 DAG\uB294 \uCD5C\uC18C \uD558\uB098\uC758 \uC704\uC0C1 \uBC30\uC5F4\uC744 \uAC00\uC9C0\uACE0 \uC788\uB2E4. \uADF8\uB9AC\uACE0 \uC54C\uACE0\uB9AC\uC998\uC740 \uC5B4\uB5A4 DAG \uC18D \uC120\uD615 \uC2DC\uAC04\uC758 \uC704\uC0C1 \uBC30\uC5F4\uC774 \uAD6C\uC131\uD55C\uB2E4\uACE0 \uC54C\uB824\uC838 \uC788\uB2E4. \uC704\uC0C1 \uC815\uB82C\uC740 feedback arc set \uC640 \uAC19\uC740 \uB7AD\uD0B9 \uBB38\uC81C\uB97C \uD574\uACB0\uD558\uB294\uB370 \uB9CE\uC774 \uC0AC\uC6A9\uB41C\uB2E4. \uC704\uC0C1 \uC815\uB82C\uC740 \uC2EC\uC9C0\uC5B4 DAG\uC758 \uC694\uC18C\uAC00 \uC5F0\uACB0\uB418\uC9C0 \uC54A\uC744\uC9C0\uB77C\uB3C4 \uAC00\uB2A5\uD558\uB2E4."@ko ,
		"Topologische Sortierung bezeichnet in der Mathematik eine Reihenfolge von Dingen, bei der vorgegebene Abh\u00E4ngigkeiten erf\u00FCllt sind. Anstehende T\u00E4tigkeiten einer Person etwa unterliegen einer Halbordnung: es existieren Bedingungen wie \u201ET\u00E4tigkeit A muss vor T\u00E4tigkeit B erledigt werden\u201C. Eine Reihenfolge, welche alle Bedingungen erf\u00FCllt, nennt man topologische Sortierung der Menge anstehender T\u00E4tigkeiten. Im Gegensatz zur Sortierung einer Totalordnung ist die Reihenfolge nicht eindeutig, sondern es kann mehrere M\u00F6glichkeiten geben. Wenn gegenseitige Abh\u00E4ngigkeiten bestehen, ist eine topologische Sortierung unm\u00F6glich. Aus mengentheoretischer Sicht handelt es sich bei der topologischen Sortierung um eine lineare Erweiterung einer partiellen Ordnung. 1930 zeigte Edward Szpilrajn, dass aus dem Auswahlaxiom folgt, dass sich jede partielle Ordnung zu einer linearen Ordnung erweitern l\u00E4sst. Die topologische Sortierung f\u00FCr endliche Mengen (hier wird das Auswahlaxiom nicht gebraucht) ist bei vielen Anwendungen der Informatik ein wichtiges Konzept. Bereits 1961 wurde von ein Algorithmus entwickelt, mit dem eine topologische Sortierung ganz allgemein erstellt werden kann. Zuvor waren allerdings schon Algorithmen f\u00FCr spezielle Anwendungen bekannt. Des Weiteren spielt die topologische Sortierung in der Graphentheorie bei der Untersuchung von gerichteten Graphen auf Zyklenfreiheit eine gro\u00DFe Rolle."@de ,
		"In teoria dei grafi un ordinamento topologico (in inglese topological sort) \u00E8 un ordinamento lineare di tutti i vertici di un grafo diretto. I nodi di un grafo si definiscono ordinati topologicamente se i nodi sono disposti in modo tale che ogni nodo viene prima di tutti i nodi collegati ai suoi archi uscenti.L'ordinamento topologico non \u00E8 un ordinamento totale, poich\u00E9 la soluzione pu\u00F2 non essere unica. Nel caso peggiore infatti si possono avere ordinamenti topologici diversi che corrispondono a tutte le possibili permutazioni degli nodi. \u00C8 possibile ordinare topologicamente un grafo se e solo se non contiene cicli (cio\u00E8 solo se \u00E8 un grafo aciclico diretto), e sono noti algoritmi per determinare un ordinamento topologico in tempo lineare."@it ,
		"\u0422\u043E\u043F\u043E\u043B\u043E\u0433\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0441\u043E\u0440\u0442\u0438\u0440\u043E\u0432\u043A\u0430 \u2014 \u0443\u043F\u043E\u0440\u044F\u0434\u043E\u0447\u0438\u0432\u0430\u043D\u0438\u0435 \u0432\u0435\u0440\u0448\u0438\u043D \u0431\u0435\u0441\u043A\u043E\u043D\u0442\u0443\u0440\u043D\u043E\u0433\u043E \u043E\u0440\u0438\u0435\u043D\u0442\u0438\u0440\u043E\u0432\u0430\u043D\u043D\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0430 \u0441\u043E\u0433\u043B\u0430\u0441\u043D\u043E \u0447\u0430\u0441\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u043F\u043E\u0440\u044F\u0434\u043A\u0443, \u0437\u0430\u0434\u0430\u043D\u043D\u043E\u043C\u0443 \u0440\u0435\u0431\u0440\u0430\u043C\u0438 \u043E\u0440\u0433\u0440\u0430\u0444\u0430 \u043D\u0430 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0435 \u0435\u0433\u043E \u0432\u0435\u0440\u0448\u0438\u043D."@ru ,
		"\u0422\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0435 \u0441\u043E\u0440\u0442\u0443\u0432\u0430\u043D\u043D\u044F \u2014 \u0432\u043F\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u0443\u0432\u0430\u043D\u043D\u044F \u0432\u0435\u0440\u0448\u0438\u043D \u0431\u0435\u0437\u043A\u043E\u043D\u0442\u0443\u0440\u043D\u043E\u0433\u043E \u043E\u0440\u0456\u0454\u043D\u0442\u043E\u0432\u0430\u043D\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0443 \u0437\u0433\u0456\u0434\u043D\u043E \u0437 \u0447\u0430\u0441\u0442\u043A\u043E\u0432\u0438\u043C \u043F\u043E\u0440\u044F\u0434\u043A\u043E\u043C, \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u0438\u043C \u0440\u0435\u0431\u0440\u0430\u043C\u0438 \u0446\u044C\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0443 \u043D\u0430 \u043C\u043D\u043E\u0436\u0438\u043D\u0456 \u0439\u043E\u0433\u043E \u0432\u0435\u0440\u0448\u0438\u043D."@uk ,
		"\u5728\u8BA1\u7B97\u673A\u79D1\u5B66\u9886\u57DF\uFF0C\u6709\u5411\u56FE\u7684\u62D3\u6251\u6392\u5E8F\u6216\u62D3\u64B2\u5B9A\u5E8F\u662F\u5BF9\u5176\u9876\u70B9\u7684\u4E00\u79CD\u7EBF\u6027\u6392\u5E8F\uFF0C\u4F7F\u5F97\u5BF9\u4E8E\u4ECE\u9876\u70B9\u5230\u9876\u70B9\u7684\u6BCF\u4E2A\u6709\u5411\u8FB9\uFF0C\u5728\u6392\u5E8F\u4E2D\u90FD\u5728\u4E4B\u524D\u3002 \u4F8B\u5982\uFF0C\u56FE\u5F62\u7684\u9876\u70B9\u53EF\u4EE5\u8868\u793A\u8981\u6267\u884C\u7684\u4EFB\u52A1\uFF0C\u5E76\u4E14\u8FB9\u53EF\u4EE5\u8868\u793A\u4E00\u4E2A\u4EFB\u52A1\u5FC5\u987B\u5728\u53E6\u4E00\u4E2A\u4EFB\u52A1\u4E4B\u524D\u6267\u884C\u7684\u7EA6\u675F\uFF1B\u5728\u8FD9\u4E2A\u5E94\u7528\u4E2D\uFF0C\u62D3\u6251\u6392\u5E8F\u53EA\u662F\u4E00\u4E2A\u6709\u6548\u7684\u4EFB\u52A1\u987A\u5E8F\u3002 \u5F53\u4E14\u4EC5\u5F53\u56FE\u4E2D\u6CA1\u6709\u5B9A\u5411\u73AF\u65F6\uFF08\u5373\u6709\u5411\u65E0\u73AF\u56FE\uFF09\uFF0C\u624D\u6709\u53EF\u80FD\u8FDB\u884C\u62D3\u6251\u6392\u5E8F\u3002 \u4EFB\u4F55\u6709\u5411\u65E0\u73AF\u56FE\u81F3\u5C11\u6709\u4E00\u4E2A\u62D3\u6251\u6392\u5E8F\u3002\u5DF2\u77E5\u6709\u7B97\u6CD5\u53EF\u4EE5\u5728\u7EBF\u6027\u65F6\u95F4\u5185\uFF0C\u6784\u5EFA\u4EFB\u4F55\u6709\u5411\u65E0\u73AF\u56FE\u7684\u62D3\u6251\u6392\u5E8F\u3002 \u5728\u56FE\u8BBA\u4E2D\uFF0C\u7531\u4E00\u4E2A\u6709\u5411\u65E0\u73AF\u56FE\u7684\u9876\u70B9\u7EC4\u6210\u7684\u5E8F\u5217\uFF0C\u5F53\u4E14\u4EC5\u5F53\u6EE1\u8DB3\u4E0B\u5217\u6761\u4EF6\u65F6\uFF0C\u624D\u80FD\u79F0\u4E3A\u8BE5\u56FE\u7684\u4E00\u4E2A\u62D3\u6251\u6392\u5E8F\uFF08\u82F1\u8A9E\uFF1ATopological sorting\uFF09\uFF1A 1. \n* \u5E8F\u5217\u4E2D\u5305\u542B\u6BCF\u4E2A\u9876\u70B9\uFF0C\u4E14\u6BCF\u4E2A\u9876\u70B9\u53EA\u51FA\u73B0\u4E00\u6B21\uFF1B 2. \n* \u82E5A\u5728\u5E8F\u5217\u4E2D\u6392\u5728B\u7684\u524D\u9762\uFF0C\u5219\u5728\u56FE\u4E2D\u4E0D\u5B58\u5728\u4ECEB\u5230A\u7684\u8DEF\u5F84\u3002"@zh ,
		"\u30C8\u30DD\u30ED\u30B8\u30AB\u30EB\u30BD\u30FC\u30C8\uFF08\u82F1: topological sort\uFF09\u306F\u3001\u30B0\u30E9\u30D5\u7406\u8AD6\u306B\u304A\u3044\u3066\u3001\u6709\u5411\u975E\u5DE1\u56DE\u30B0\u30E9\u30D5\uFF08\u82F1: directed acyclic graph, DAG\uFF09\u306E\u5404\u30CE\u30FC\u30C9\u3092\u9806\u5E8F\u4ED8\u3051\u3057\u3066\u3001\u3069\u306E\u30CE\u30FC\u30C9\u3082\u305D\u306E\u51FA\u529B\u8FBA\u306E\u5148\u306E\u30CE\u30FC\u30C9\u3088\u308A\u524D\u306B\u304F\u308B\u3088\u3046\u306B\u4E26\u3079\u308B\u3053\u3068\u3067\u3042\u308B\u3002\u6709\u5411\u975E\u5DE1\u56DE\u30B0\u30E9\u30D5\u306F\u5FC5\u305A\u30C8\u30DD\u30ED\u30B8\u30AB\u30EB\u30BD\u30FC\u30C8\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u6709\u5411\u975E\u5DE1\u56DE\u30B0\u30E9\u30D5\u306E\u30CE\u30FC\u30C9\u306E\u96C6\u5408\u306B\u5230\u9054\u53EF\u80FD\u6027\u95A2\u4FC2 R (\u30CE\u30FC\u30C9 x \u304B\u3089 y \u3078\u306E(\u5404\u8FBA\u306E\u5411\u304D\u306B\u9006\u884C\u3057\u306A\u3044)\u7D4C\u8DEF\u304C\u5B58\u5728\u3059\u308B\u3068\u304D\u3001\u307E\u305F\u305D\u306E\u3068\u304D\u306B\u9650\u308A xRy \u3068\u3059\u308B)\u3092\u5B9A\u3081\u308B\u3068\u3001R \u306F\u534A\u9806\u5E8F\u95A2\u4FC2\u3068\u306A\u308B\u3002\u30C8\u30DD\u30ED\u30B8\u30AB\u30EB\u30BD\u30FC\u30C8\u3068\u306F\u3001\u3053\u306E R \u3092\u5168\u9806\u5E8F\u306B\u306A\u308B\u3088\u3046\u306B\u62E1\u5F35\u3057\u305F\u3082\u306E\u3068\u307F\u306A\u305B\u308B\u3002"@ja ,
		"Una ordenaci\u00F3n topol\u00F3gica (topological sort, topological ordering, topsort o toposort en ingl\u00E9s) de un grafo ac\u00EDclico dirigido G es una ordenaci\u00F3n lineal de todos los nodos de G que satisface que si G contiene la arista dirigida uv entonces el nodo u aparece antes del nodo v. La condici\u00F3n que el grafo no contenga ciclos es importante, ya que no se puede obtener ordenaci\u00F3n topol\u00F3gica de grafos que contengan ciclos. Usualmente, para clarificar el concepto se suelen identificar los nodos con tareas a realizar en la que hay una precedencia a la hora de ejecutar dichas tareas. La ordenaci\u00F3n topol\u00F3gica por tanto es una lista en orden lineal en que deben realizarse las tareas. Para poder encontrar la ordenaci\u00F3n topol\u00F3gica del grafo G deberemos aplicar una modificaci\u00F3n del algoritmo de b\u00FAsqueda en profundidad (DFS)."@es ,
		"\u03A4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AE \u03C4\u03B1\u03BE\u03B9\u03BD\u03CC\u03BC\u03B7\u03C3\u03B7 \u03AE \u03B1\u03BB\u03BB\u03B9\u03CE\u03C2 \u03C4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AE \u03B4\u03B9\u03AC\u03C4\u03B1\u03BE\u03B7 (\u03B1\u03B3\u03B3\u03BB\u03B9\u03BA\u03AC: Topological sorting) \u03B5\u03BD\u03CC\u03C2 \u039A\u03B1\u03C4\u03B5\u03C5\u03B8\u03C5\u03BD\u03CC\u03BC\u03B5\u03BD\u03BF\u03C5 \u0386\u03BA\u03C5\u03BA\u03BB\u03BF\u03C5 \u0393\u03C1\u03AC\u03C6\u03BF\u03C5 (Directed Acyclic Graph \u03AE DAG), \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03C3\u03C4\u03B7 \u0398\u03B5\u03C9\u03C1\u03AF\u03B1 \u0393\u03C1\u03AC\u03C6\u03C9\u03BD \u03B7 \u03B3\u03C1\u03B1\u03BC\u03BC\u03B9\u03BA\u03AE \u03B4\u03B9\u03AC\u03C4\u03B1\u03BE\u03B7 \u03C4\u03C9\u03BD \u03BA\u03CC\u03BC\u03B2\u03C9\u03BD, \u03AD\u03C4\u03C3\u03B9 \u03CE\u03C3\u03C4\u03B5 \u03BA\u03AC\u03B8\u03B5 \u03C0\u03C1\u03CC\u03B3\u03BF\u03BD\u03BF\u03C2 \u03B5\u03BD\u03CC\u03C2 v \u03C0\u03C1\u03BF\u03B7\u03B3\u03B5\u03AF\u03C4\u03B1\u03B9 \u03C4\u03BF\u03C5 v \u03C3\u03C4\u03B7 \u03B4\u03B9\u03AC\u03C4\u03B1\u03BE\u03B7. \u039A\u03AC\u03B8\u03B5 \u039A\u03B1\u03C4\u03B5\u03C5\u03B8\u03C5\u03BD\u03CC\u03BC\u03B5\u03BD\u03BF\u03C2 \u0386\u03BA\u03C5\u03BA\u03BB\u03BF\u03C2 \u0393\u03C1\u03AC\u03C6\u03BF\u03C2 \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03AD\u03C7\u03B5\u03B9 \u03BC\u03AF\u03B1 \u03AE \u03C0\u03B5\u03C1\u03B9\u03C3\u03C3\u03CC\u03C4\u03B5\u03C1\u03B5\u03C2 \u03C4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AD\u03C2 \u03B4\u03B9\u03B1\u03C4\u03AC\u03BE\u03B5\u03B9\u03C2. \u03A0\u03B9\u03BF \u03B1\u03C5\u03C3\u03C4\u03B7\u03C1\u03AC, \u03BC\u03C0\u03BF\u03C1\u03BF\u03CD\u03BC\u03B5 \u03BD\u03B1 \u03BF\u03C1\u03AF\u03C3\u03BF\u03C5\u03BC\u03B5 \u03C4\u03B7\u03BD \u03C4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AE \u03C4\u03B1\u03BE\u03B9\u03BD\u03CC\u03BC\u03B7\u03C3\u03B7 \u03B5\u03BD\u03CC\u03C2 \u039A\u03B1\u03C4\u03B5\u03C5\u03B8\u03C5\u03BD\u03CC\u03BC\u03B5\u03BD\u03BF\u03C5 \u0386\u03BA\u03C5\u03BA\u03BB\u03BF\u03C5 \u0393\u03C1\u03AC\u03C6\u03BF\u03C5 G(V, E), \u03BC\u03B5 V \u03C4\u03BF \u03C3\u03CD\u03BD\u03BF\u03BB\u03BF \u03C4\u03C9\u03BD \u03BA\u03CC\u03BC\u03B2\u03C9\u03BD \u03BA\u03B1\u03B9 E \u03C4\u03BF \u03C3\u03CD\u03BD\u03BF\u03BB\u03BF \u03C4\u03C9\u03BD \u03C9\u03C2 \u03BC\u03AF\u03B1 \u03B3\u03C1\u03B1\u03BC\u03BC\u03B9\u03BA\u03AE \u03B1\u03BB\u03BB\u03B7\u03BB\u03BF\u03C5\u03C7\u03AF\u03B1 \u03C4\u03C9\u03BD \u03BA\u03CC\u03BC\u03B2\u03C9\u03BD V, \u03AD\u03C4\u03C3\u03B9 \u03CE\u03C3\u03C4\u03B5 \u03B1\u03BD (u, v) E, \u03C0(u) < \u03C0(v), \u03CC\u03C0\u03BF\u03C5 \u03C0(x) \u03B7 \u03B8\u03AD\u03C3\u03B7 \u03C3\u03C4\u03B7\u03BD \u03BF\u03C0\u03BF\u03AF\u03B1 \u03B2\u03C1\u03AF\u03C3\u03BA\u03B5\u03C4\u03B1\u03B9 \u03BF \u03BA\u03CC\u03BC\u03B2\u03BF\u03C2 x \u03C3\u03C4\u03B7 \u03B4\u03B9\u03AC\u03C4\u03B1\u03BE\u03B7."@el ,
		"En th\u00E9orie des graphes, et plus sp\u00E9cialement en algorithmique des graphes, un tri topologique d'un graphe acyclique orient\u00E9 (ou dag, de l'anglais directed acyclic graph) est un ordre total sur l'ensemble des sommets, dans lequel s pr\u00E9c\u00E8de t pour tout arc d'un sommet s \u00E0 un sommet t. En d'autres termes, un tri topologique est une extension lin\u00E9aire de l'ordre partiel sur les sommets d\u00E9termin\u00E9s par les arcs."@fr ;
	dbo:wikiPageWikiLink	dbr:Instruction_scheduling ,
		dbr:Shortest_path_problem ,
		dbr:Directed_graph ,
		dbr:Makefile ,
		dbr:Comparison_sort ,
		dbc:Directed_acyclic_graphs ,
		dbr:Weighted_graph ,
		<http://dbpedia.org/resource/Connectivity_(graph_theory)> ,
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		<http://dbpedia.org/resource/D._E._Knuth> ,
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		dbc:Graph_algorithms ,
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		dbc:Articles_with_example_pseudocode ,
		dbr:Feedback_arc_set ,
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		dbr:Dependency_graph ,
		<http://dbpedia.org/resource/Tarjan\u0027s_strongly_connected_components_algorithm> ,
		dbr:Critical_path_method ,
		<http://dbpedia.org/resource/Coffman\u2013Graham_algorithm> ,
		dbr:Reachability ,
		dbr:Transitive_reduction ,
		<http://dbpedia.org/resource/File:Parallel_Topological_Sorting.gif> ,
		dbr:Logic_synthesis ,
		dbr:Algorithm ,
		dbr:CRCW_PRAM ,
		dbr:Indegree ,
		dbr:Serialization ,
		dbr:SPMD ,
		dbr:Min-plus_matrix_multiplication ,
		dbr:Parallel_random-access_machine ,
		dbr:Distributed_memory ,
		dbr:The_Art_of_Computer_Programming ,
		dbr:Lexicographic_order ,
		<http://dbpedia.org/resource/NC_(complexity)> ,
		dbr:Prefix_sum ,
		dbr:Tsort ,
		dbr:Depth-first_search ,
		dbc:Sorting_algorithms ,
		dbr:Transitive_relation ,
		<http://dbpedia.org/resource/File:Directed_acyclic_graph_2.svg> ,
		dbr:Project_management ,
		dbr:Partial_order ,
		dbr:Job_shop_scheduling ,
		<http://dbpedia.org/resource/Linker_(computing)> ,
		dbr:Directed_cycle ,
		dbr:Total_order ,
		<http://dbpedia.org/resource/Vertex_(graph_theory)> ,
		dbr:Directed_acyclic_graph ,
		dbr:Layered_graph_drawing ,
		dbr:Linear_extension ,
		dbr:Linear_time .
@prefix dbp:	<http://dbpedia.org/property/> .
@prefix dbt:	<http://dbpedia.org/resource/Template:> .
dbr:Topological_sorting	dbp:wikiPageUsesTemplate	dbt:Sorting ,
		dbt:Distinguish ,
		dbt:Harvp ,
		dbt:Framebox ,
		dbt:R ,
		dbt:Frame-footer ,
		dbt:Mvar ,
		dbt:Short_description ,
		dbt:Math ,
		dbt:Reflist ,
		dbt:Tmath ,
		dbt:Mset ,
		dbt:Redirect ,
		dbt:Mono ,
		dbt:MathWorld ,
		<http://dbpedia.org/resource/Template:=> ;
	dbo:thumbnail	<http://commons.wikimedia.org/wiki/Special:FilePath/Directed_acyclic_graph_2.svg?width=300> ;
	dbo:wikiPageRevisionID	1123299686 ;
	dbo:wikiPageExternalLink	<https://xlinux.nist.gov/dads/HTML/topologicalSort.html> .
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	dbo:wikiPageID	897064 ;
	dbp:title	"Topological Sort"@en ;
	owl:sameAs	<http://es.dbpedia.org/resource/Ordenamiento_topol\u00F3gico> ,
		<http://uk.dbpedia.org/resource/\u0422\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0435_\u0441\u043E\u0440\u0442\u0443\u0432\u0430\u043D\u043D\u044F> ,
		<http://el.dbpedia.org/resource/\u03A4\u03BF\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03BA\u03AE_\u03C4\u03B1\u03BE\u03B9\u03BD\u03CC\u03BC\u03B7\u03C3\u03B7> ,
		dbr:Topological_sorting ,
		<http://vi.dbpedia.org/resource/S\u1EAFp_x\u1EBFp_t\u00F4_p\u00F4> .
@prefix dbpedia-it:	<http://it.dbpedia.org/resource/> .
dbr:Topological_sorting	owl:sameAs	dbpedia-it:Ordinamento_topologico .
@prefix dbpedia-no:	<http://no.dbpedia.org/resource/> .
dbr:Topological_sorting	owl:sameAs	dbpedia-no:Topologisk_sortering ,
		<http://ja.dbpedia.org/resource/\u30C8\u30DD\u30ED\u30B8\u30AB\u30EB\u30BD\u30FC\u30C8> .
@prefix dbpedia-fi:	<http://fi.dbpedia.org/resource/> .
dbr:Topological_sorting	owl:sameAs	dbpedia-fi:Topologinen_lajittelu ,
		<http://he.dbpedia.org/resource/\u05DE\u05D9\u05D5\u05DF_\u05D8\u05D5\u05E4\u05D5\u05DC\u05D5\u05D2\u05D9> ,
		<http://pt.dbpedia.org/resource/Ordena\u00E7\u00E3o_topol\u00F3gica> ,
		<http://ko.dbpedia.org/resource/\uC704\uC0C1\uC815\uB82C> .
@prefix dbpedia-hu:	<http://hu.dbpedia.org/resource/> .
dbr:Topological_sorting	owl:sameAs	dbpedia-hu:Topologikus_sorrend ,
		<https://global.dbpedia.org/id/4v6KU> ,
		<http://ru.dbpedia.org/resource/\u0422\u043E\u043F\u043E\u043B\u043E\u0433\u0438\u0447\u0435\u0441\u043A\u0430\u044F_\u0441\u043E\u0440\u0442\u0438\u0440\u043E\u0432\u043A\u0430> .
@prefix yago-res:	<http://yago-knowledge.org/resource/> .
dbr:Topological_sorting	owl:sameAs	yago-res:Topological_sorting ,
		<http://rdf.freebase.com/ns/m.03mt02> ,
		<http://sr.dbpedia.org/resource/Topolo\u0161ko_ure\u0111enje> ,
		<http://fa.dbpedia.org/resource/\u0645\u0631\u062A\u0628\u200C\u0633\u0627\u0632\u06CC_\u062A\u0648\u067E\u0648\u0644\u0648\u0698\u06CC\u06A9\u06CC> .
@prefix dbpedia-fr:	<http://fr.dbpedia.org/resource/> .
dbr:Topological_sorting	owl:sameAs	dbpedia-fr:Tri_topologique .
@prefix dbpedia-de:	<http://de.dbpedia.org/resource/> .
dbr:Topological_sorting	owl:sameAs	dbpedia-de:Topologische_Sortierung .
@prefix wikidata:	<http://www.wikidata.org/entity/> .
dbr:Topological_sorting	owl:sameAs	wikidata:Q753127 .
@prefix dbpedia-pl:	<http://pl.dbpedia.org/resource/> .
dbr:Topological_sorting	owl:sameAs	dbpedia-pl:Sortowanie_topologiczne ,
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@prefix prov:	<http://www.w3.org/ns/prov#> .
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dbr:Tree_traversal	dbo:wikiPageWikiLink	dbr:Topological_sorting .
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dbr:Certifying_algorithm	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Package_manager	dbo:wikiPageWikiLink	dbr:Topological_sorting .
<http://dbpedia.org/resource/2-satisfiability>	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:The_Art_of_Computer_Programming	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:List_of_algorithms	dbo:wikiPageWikiLink	dbr:Topological_sorting .
<http://dbpedia.org/resource/\u266FP-complete>	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Reactive_programming	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Longest_path_problem	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Feedback_arc_set	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Alexander_Skopin	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Topological_sort	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
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dbr:Tsort	dbo:wikiPageWikiLink	dbr:Topological_sorting .
dbr:Top_sort	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
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dbr:Topological_labelling	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
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dbr:Toposort	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
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dbr:Topsort	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
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dbr:Dependency_resolver	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
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dbr:Parallel_algorithms_for_topological_sorting	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
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dbr:Algorithms_for_topological_sorting	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
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dbr:Dependency_resolution	dbo:wikiPageWikiLink	dbr:Topological_sorting ;
	dbo:wikiPageRedirects	dbr:Topological_sorting .  <script>parent.window.postMessage('ixistenz.url:http://dbpedia.org/data/Topological_sorting.n3', '*'); </script> <div id='browserdiffcontainer' style='position: fixed; right: 10px; top: 10vh; min-width: 60px;  border: 1px solid white; background: rgb(251, 189, 0);; opacity: 0.9; font-family: helvetica, arial, sans serif;  font-size: 12px; z-index: 20001; padding-bottom: 20px;'><div onclick="toggle('browserdiffcontainerlist'); return false;" style='background: rgb(151, 89, 0);; color: white; '><strong>&nbsp; <span class='glyphicon glyphicon-minus'></span> NODES</strong></div><div id='browserdiffcontainerlist' style='padding-left: 10px; padding-right: 5px; max-height: 50vh; overflow: auto; '><div><a href='#diffid115' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:115', '*');; return false;" style='text-decoration: none; '>Project </a> <a style='color: white;' href='#diffid115'><sup>1</sup></a></div><div><a href='#diffid122' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:122', '*');; return false;" style='text-decoration: none; '>todo </a> <a style='color: white;' href='#diffid122'><sup>4</sup></a></div></div></div>
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