[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7041#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7041","headline":"\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5 – Wikipedia","name":"\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5 – Wikipedia","description":"\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306e\u4f8b \u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3001\u6709\u5411\u975e\u5faa\u74b0\u30b0\u30e9\u30d5\u3001\u6709\u5411\u7121\u9589\u8def\u30b0\u30e9\u30d5\uff08\u3086\u3046\u3053\u3046\u3072\u3058\u3085\u3093\u304b\u3044\u30b0\u30e9\u30d5\u3001\u82f1: Directed acyclic graph, DAG\uff09\u3068\u306f\u3001\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u304a\u3051\u308b\u9589\u8def\u306e\u306a\u3044\u6709\u5411\u30b0\u30e9\u30d5\u306e\u3053\u3068\u3067\u3042\u308b\u3002\u6709\u5411\u30b0\u30e9\u30d5\u306f\u9802\u70b9\u3068\u6709\u5411\u8fba\uff08\u65b9\u5411\u3092\u793a\u3059\u77e2\u5370\u4ed8\u304d\u306e\u8fba\uff09\u304b\u3089\u306a\u308a\u3001\u8fba\u306f\u9802\u70b9\u540c\u58eb\u3092\u3064\u306a\u3050\u304c\u3001\u3042\u308b\u9802\u70b9 v{displaystyle v} \u304b\u3089\u51fa\u767a\u3057\u3001\u8fba\u3092\u305f\u3069\u308a\u3001\u9802\u70b9 v{displaystyle v} \u306b\u623b\u3063\u3066\u3053\u306a\u3044\u306e\u304c\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3067\u3042\u308b[1][2][3]\u3002 \u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u69d8\u3005\u306a\u60c5\u5831\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u306e\u306b\u4f7f\u308f\u308c\u308b\u3002\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306b\u304a\u3051\u308b\u5230\u9054\u53ef\u80fd\u6027\u306f\u534a\u9806\u5e8f\u3092\u69cb\u6210\u3057\u3001\u5168\u3066\u306e\u6709\u9650\u534a\u9806\u5e8f\u306f\u5230\u9054\u53ef\u80fd\u6027\u3092\u5229\u7528\u3057\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3067\u8868\u73fe\u53ef\u80fd\u3067\u3042\u308b\u3002\u9806\u5e8f\u3065\u3051\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u30bf\u30b9\u30af\u306e\u96c6\u5408\u306f\u3001\u3042\u308b\u30bf\u30b9\u30af\u304c\u4ed6\u306e\u30bf\u30b9\u30af\u3088\u308a\u3082\u524d\u306b\u884c\u3046\u5fc5\u8981\u304c\u3042\u308b\u3068\u3044\u3046\u5236\u7d04\u306b\u3088\u308a\u3001\u9802\u70b9\u3092\u30bf\u30b9\u30af\u3001\u8fba\u3092\u5236\u7d04\u6761\u4ef6\u3067\u8868\u73fe\u3059\u308b\u3068\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3067\u8868\u73fe\u3067\u304d\u308b\u3002\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u30bd\u30fc\u30c8\u3092\u4f7f\u3046\u3068\u3001\u59a5\u5f53\u306a\u9806\u5e8f\u3092\u624b\u306b\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u52a0\u3048\u3066\u3001\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u4e00\u90e8\u304c\u91cd\u306a\u308b\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u96c6\u5408\u3092\u8868\u73fe\u3059\u308b\u969b\u306e\u7a7a\u9593\u52b9\u7387\u306e\u826f\u3044\u8868\u73fe\u3068\u3057\u3066\u5229\u7528\u3067\u304d\u308b\u3002\u307e\u305f\u3001\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u30a4\u30d9\u30f3\u30c8\u9593\u306e\u56e0\u679c\u95a2\u4fc2\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u306b\u3082\u4f7f\u3048\u308b\u3002\u3055\u3089\u306b\u3001\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u30c7\u30fc\u30bf\u306e\u6d41\u308c\u304c\u4e00\u5b9a\u65b9\u5411\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u306b\u3082\u4f7f\u3048\u308b\u3002 \u7121\u5411\u30b0\u30e9\u30d5\u306b\u304a\u3051\u308b\u5bfe\u5fdc\u3059\u308b\u6982\u5ff5\u306f\u68ee\u3067\u3001\u68ee\u306f\u9589\u8def\u306e\u306a\u3044\u7121\u5411\u30b0\u30e9\u30d5\u3067\u3042\u308b\u3002\u68ee\u304b\u3089\u65b9\u5411\u3092\u9078\u3076\u3068polytree\u3068\u547c\u3070\u308c\u308b\u7279\u6b8a\u306a\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001\u7121\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\uff08\u68ee\uff09\u306b\u65b9\u5411\u4ed8\u3051\u3059\u308b\u65b9\u6cd5\u3067\u306f\u4f5c\u308c\u306a\u3044\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u304c\u3042\u308a\u3001\u5168\u3066\u306e\u7121\u5411\u30b0\u30e9\u30d5\u306facyclic orientation\u304c\u3042\u308b\u305f\u3081\u3001\u8fba\u306b\u65b9\u5411\u4ed8\u3051\u308b\u3068\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306b\u306a\u308b\u3002\u3053\u306e\u7406\u7531\u304b\u3089\u3001directed acyclic graph\u3068\u547c\u3076\u3088\u308a\u3082acyclic directed graph\u3068\u547c\u3076\u65b9\u304c\u6b63\u78ba\u3067\u3042\u308b\u3002 \u306a\u304a\u3001\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3092\u30d7\u30ed\u30c8\u30b3\u30eb\u3068\u3057\u305f\u4eee\u60f3\u901a\u8ca8\u306b\u306f\u3001BYTEBALL\u3001IOTA\u3001ADK\u304c\u3042\u308b[4][5][6][7][8]\u3002","datePublished":"2019-02-25","dateModified":"2019-02-25","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/39\/Directed_acyclic_graph_3.svg\/356px-Directed_acyclic_graph_3.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/39\/Directed_acyclic_graph_3.svg\/356px-Directed_acyclic_graph_3.svg.png","height":"256","width":"356"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7041","about":["Wiki"],"wordCount":3905,"articleBody":"  \u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306e\u4f8b\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3001\u6709\u5411\u975e\u5faa\u74b0\u30b0\u30e9\u30d5\u3001\u6709\u5411\u7121\u9589\u8def\u30b0\u30e9\u30d5\uff08\u3086\u3046\u3053\u3046\u3072\u3058\u3085\u3093\u304b\u3044\u30b0\u30e9\u30d5\u3001\u82f1: Directed acyclic graph, DAG\uff09\u3068\u306f\u3001\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u304a\u3051\u308b\u9589\u8def\u306e\u306a\u3044\u6709\u5411\u30b0\u30e9\u30d5\u306e\u3053\u3068\u3067\u3042\u308b\u3002\u6709\u5411\u30b0\u30e9\u30d5\u306f\u9802\u70b9\u3068\u6709\u5411\u8fba\uff08\u65b9\u5411\u3092\u793a\u3059\u77e2\u5370\u4ed8\u304d\u306e\u8fba\uff09\u304b\u3089\u306a\u308a\u3001\u8fba\u306f\u9802\u70b9\u540c\u58eb\u3092\u3064\u306a\u3050\u304c\u3001\u3042\u308b\u9802\u70b9v{displaystyle v}\u304b\u3089\u51fa\u767a\u3057\u3001\u8fba\u3092\u305f\u3069\u308a\u3001\u9802\u70b9v{displaystyle v}\u306b\u623b\u3063\u3066\u3053\u306a\u3044\u306e\u304c\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3067\u3042\u308b[1][2][3]\u3002\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u69d8\u3005\u306a\u60c5\u5831\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u306e\u306b\u4f7f\u308f\u308c\u308b\u3002\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306b\u304a\u3051\u308b\u5230\u9054\u53ef\u80fd\u6027\u306f\u534a\u9806\u5e8f\u3092\u69cb\u6210\u3057\u3001\u5168\u3066\u306e\u6709\u9650\u534a\u9806\u5e8f\u306f\u5230\u9054\u53ef\u80fd\u6027\u3092\u5229\u7528\u3057\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3067\u8868\u73fe\u53ef\u80fd\u3067\u3042\u308b\u3002\u9806\u5e8f\u3065\u3051\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u30bf\u30b9\u30af\u306e\u96c6\u5408\u306f\u3001\u3042\u308b\u30bf\u30b9\u30af\u304c\u4ed6\u306e\u30bf\u30b9\u30af\u3088\u308a\u3082\u524d\u306b\u884c\u3046\u5fc5\u8981\u304c\u3042\u308b\u3068\u3044\u3046\u5236\u7d04\u306b\u3088\u308a\u3001\u9802\u70b9\u3092\u30bf\u30b9\u30af\u3001\u8fba\u3092\u5236\u7d04\u6761\u4ef6\u3067\u8868\u73fe\u3059\u308b\u3068\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3067\u8868\u73fe\u3067\u304d\u308b\u3002\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u30bd\u30fc\u30c8\u3092\u4f7f\u3046\u3068\u3001\u59a5\u5f53\u306a\u9806\u5e8f\u3092\u624b\u306b\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u52a0\u3048\u3066\u3001\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u4e00\u90e8\u304c\u91cd\u306a\u308b\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u96c6\u5408\u3092\u8868\u73fe\u3059\u308b\u969b\u306e\u7a7a\u9593\u52b9\u7387\u306e\u826f\u3044\u8868\u73fe\u3068\u3057\u3066\u5229\u7528\u3067\u304d\u308b\u3002\u307e\u305f\u3001\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u30a4\u30d9\u30f3\u30c8\u9593\u306e\u56e0\u679c\u95a2\u4fc2\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u306b\u3082\u4f7f\u3048\u308b\u3002\u3055\u3089\u306b\u3001\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u30c7\u30fc\u30bf\u306e\u6d41\u308c\u304c\u4e00\u5b9a\u65b9\u5411\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u306b\u3082\u4f7f\u3048\u308b\u3002\u7121\u5411\u30b0\u30e9\u30d5\u306b\u304a\u3051\u308b\u5bfe\u5fdc\u3059\u308b\u6982\u5ff5\u306f\u68ee\u3067\u3001\u68ee\u306f\u9589\u8def\u306e\u306a\u3044\u7121\u5411\u30b0\u30e9\u30d5\u3067\u3042\u308b\u3002\u68ee\u304b\u3089\u65b9\u5411\u3092\u9078\u3076\u3068polytree\u3068\u547c\u3070\u308c\u308b\u7279\u6b8a\u306a\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001\u7121\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\uff08\u68ee\uff09\u306b\u65b9\u5411\u4ed8\u3051\u3059\u308b\u65b9\u6cd5\u3067\u306f\u4f5c\u308c\u306a\u3044\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u304c\u3042\u308a\u3001\u5168\u3066\u306e\u7121\u5411\u30b0\u30e9\u30d5\u306facyclic orientation\u304c\u3042\u308b\u305f\u3081\u3001\u8fba\u306b\u65b9\u5411\u4ed8\u3051\u308b\u3068\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306b\u306a\u308b\u3002\u3053\u306e\u7406\u7531\u304b\u3089\u3001directed acyclic graph\u3068\u547c\u3076\u3088\u308a\u3082acyclic directed graph\u3068\u547c\u3076\u65b9\u304c\u6b63\u78ba\u3067\u3042\u308b\u3002\u306a\u304a\u3001\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3092\u30d7\u30ed\u30c8\u30b3\u30eb\u3068\u3057\u305f\u4eee\u60f3\u901a\u8ca8\u306b\u306f\u3001BYTEBALL\u3001IOTA\u3001ADK\u304c\u3042\u308b[4][5][6][7][8]\u3002\u30b0\u30e9\u30d5\u306f\u3001\u9802\u70b9\uff08vertex\uff09\u3068\u30012 \u3064\u306e\u9802\u70b9\u3092\u7d50\u3076\u8fba\uff08edge\uff09\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u3002\u9802\u70b9\u306f\u3001\u8fba\u306b\u3088\u3063\u3066\u30da\u30a2\u3067\u63a5\u7d9a\u3055\u308c\u308b\u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3042\u308b\u3002\u6709\u5411\u30b0\u30e9\u30d5\u306e\u5834\u5408\u3001\u5404\u8fba\u306f\u3042\u308b\u9802\u70b9\u304b\u3089\u5225\u306e\u9802\u70b9\u3078\u306e\u65b9\u5411\u6027\u3092\u6301\u3064\u3002\u6709\u5411\u30b0\u30e9\u30d5\u306e\u7d4c\u8def\uff08path\uff09\u3068\u306f\u3001\u5404\u8fba\u306e\u7d42\u70b9\u3068\u306a\u308b\u9802\u70b9\u304c\u6b21\u306e\u8fba\u306e\u59cb\u70b9\u3068\u306a\u308b\u9802\u70b9\u3068\u540c\u3058\u3067\u3042\u308b\u3068\u3044\u3046\u6027\u8cea\u3092\u6301\u3064\u8fba\u306e\u5217\u3067\u3042\u308b\u3002\u7d4c\u8def\u306f\u3001\u305d\u306e\u6700\u521d\u306e\u8fba\u306e\u59cb\u70b9\u3068\u306a\u308b\u9802\u70b9\u304c\u6700\u5f8c\u306e\u8fba\u306e\u7d42\u70b9\u3068\u306a\u308b\u9802\u70b9\u3068\u540c\u3058\u3067\u3042\u308b\u3068\u304d\u3001\u30b5\u30a4\u30af\u30eb\uff08\u9589\u8def\uff09\u3092\u5f62\u6210\u3059\u308b\u3002\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u306f\u3001\u30b5\u30a4\u30af\u30eb\u3092\u6301\u305f\u306a\u3044\u6709\u5411\u30b0\u30e9\u30d5\u306e\u3053\u3068\u3067\u3042\u308b[9][10][11]\u3002\u6709\u5411\u30b0\u30e9\u30d5\u306e\u9802\u70b9 v \u306f\u3001\u9802\u70b9 u \u3092\u59cb\u70b9\u3068\u3057\u9802\u70b9 v \u3092\u7d42\u70b9\u3068\u3059\u308b\u7d4c\u8def\u304c\u5b58\u5728\u3059\u308b\u3068\u304d\u3001\u9802\u70b9 u \u304b\u3089\u5230\u9054\u53ef\u80fd\u3067\u3042\u308b\u3068\u3044\u3046\u3002\u7279\u5225\u306a\u4f8b\u3068\u3057\u3066\u3001\u3059\u3079\u3066\u306e\u9802\u70b9\u306f\u3001\u81ea\u5206\u81ea\u8eab\u304b\u3089\uff08\u8fba\u304c\u306e\u6570\u304c 0 \u306e\u7d4c\u8def\u306b\u3088\u3063\u3066\uff09\u5230\u9054\u53ef\u80fd\u3067\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u308b\u3002\u3042\u308b\u9802\u70b9\u304c\u3001\u975e\u81ea\u660e\u306a\u7d4c\u8def\uff08\u8fba\u306e\u6570\u304c 1 \u3064\u4ee5\u4e0a\u306e\u7d4c\u8def\uff09\u3067\u81ea\u8eab\u306b\u5230\u9054\u3067\u304d\u308b\u5834\u5408\u3001\u305d\u306e\u7d4c\u8def\u306f\u30b5\u30a4\u30af\u30eb\u3067\u3042\u308b\u3002\u3053\u306e\u305f\u3081\u3001\u3069\u306e\u9802\u70b9\u3082\u975e\u81ea\u660e\u306a\u7d4c\u8def\u3067\u306f\u81ea\u8eab\u306b\u5230\u9054\u3067\u304d\u306a\u3044\u30b0\u30e9\u30d5\u3001\u3068\u3057\u3066\u3082\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b[12]\u3002\u6570\u5b66\u7684\u7279\u6027[\u7de8\u96c6]\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u30fb\u63a8\u79fb\u9589\u5305\u30fb\u63a8\u79fb\u7c21\u7d04[\u7de8\u96c6]DAG \u306b\u304a\u3051\u308b\u5230\u9054\u53ef\u80fd\u6027\uff08\u82f1\u8a9e\u7248\uff09\u95a2\u4fc2\u306f\u3001 DAG \u306e\u9802\u70b9\u306e\u534a\u9806\u5e8f \u2264 \u3068\u3057\u3066\u5f62\u5f0f\u5316\u3067\u304d\u308b\u3002\u3053\u306e\u534a\u9806\u5e8f\u3067\u306f\u3001\u9802\u70b9 u \u3068\u9802\u70b9 v \u306f\u3001DAG \u5185\u306b u \u304b\u3089 v \u3078\u306e\u6709\u5411\u30d1\u30b9\u304c\u5b58\u5728\u3059\u308b\u3068\u304d\u3001\u3059\u306a\u308f\u3061 v \u304c u \u304b\u3089\u5230\u9054\u53ef\u80fd\u306a\u3068\u304d\u306b\u3001 u \u2264 v \u3068\u3057\u3066\u9806\u5e8f\u3065\u3051\u3089\u308c\u308b[13]\u3002\u3057\u304b\u3057\u3001\u7570\u306a\u308b DAG \u304b\u3089\u3001\u540c\u3058\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u3068\u540c\u3058\u534a\u9806\u5e8f\u96c6\u5408\u304c\u5f97\u3089\u308c\u308b\u5834\u5408\u3082\u3042\u308b[14]\u3002\u4f8b\u3048\u3070\u30012 \u3064\u306e\u8fba a \u2192 b\u3001b \u2192 c \u3092\u6301\u3064 DAG \u306f\u30013 \u3064\u306e\u8fba a \u2192 b\u3001b \u2192 c\u3001a \u2192 c \u3092\u6301\u3064 DAG \u3068\u540c\u3058\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u3092\u6301\u3061\u3001\u3069\u3061\u3089\u3082\u9802\u70b9\u304c a \u2264 b \u2264 c \u306e\u9806\u306b\u4e26\u3093\u3060\u534a\u9806\u5e8f\u96c6\u5408\u3092\u6301\u3064\u3002\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5 GG \u306e\u63a8\u79fb\u7c21\u7d04DAG G \u306e\u63a8\u79fb\u9589\u5305\u306f\u3001G \u3068\u540c\u3058\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u3092\u8868\u3059 DAG \u306e\u4e2d\u3067\u3001\u6700\u3082\u591a\u304f\u306e\u8fba\u3092\u6301\u3064\u3082\u306e\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u3001\u9802\u70b9 u \u304b\u3089 v \u306b\u5230\u9054\u3067\u304d\u308b\u3068\u304d\u306b\u306f\u5fc5\u305a\u8fba u \u2192 v \u3092\u6301\u3064\u3002\u3064\u307e\u308a\u3001G \u306e\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u306b\u304a\u3044\u3066\u7570\u306a\u308b\u8981\u7d20\u306e\u95a2\u9023\u3059\u308b\u30da\u30a2 u \u2264 v \u306f\u5fc5\u305a\u8fba\u3092\u6301\u3064\u306e\u3067\u3001\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2 \u2264 \u3092\u30b0\u30e9\u30d5\u7406\u8ad6\u7684\u306b\u76f4\u8a33\u3057\u305f\u3082\u306e\u3068\u8003\u3048\u3066\u3088\u3044\u3002\u3053\u306e\u65b9\u6cd5\u306f\u3088\u308a\u4e00\u822c\u7684\u306b\u6709\u52b9\u3067\u3001\u5168\u3066\u306e\u6709\u9650\u534a\u9806\u5e8f\u96c6\u5408\uff08S\u3001\u2264\uff09\u306b\u5bfe\u3057\u3066\u3001S \u306e\u5404\u30e1\u30f3\u30d0\u30fc\u306b\u9802\u70b9\u3092\u6301\u3061\u3001u \u2264 v \u3067\u95a2\u9023\u3059\u308b\u8981\u7d20\u306e\u30da\u30a2\u306b\u8fba\u3092\u6301\u3064\u30b0\u30e9\u30d5\u306f\u3001\u81ea\u52d5\u7684\u306b DAG \u306e\u63a8\u79fb\u9589\u5305\u3068\u306a\u308a\u3001\uff08S\u3001\u2264\uff09\u3092\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u3068\u3057\u3066\u6301\u3064\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u5168\u3066\u306e\u6709\u9650\u534a\u9806\u5e8f\u96c6\u5408\u306f\u3001DAG \u306e\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002DAG G \u306e\u63a8\u79fb\u7c21\u7d04\uff08\u82f1\u8a9e\u7248\uff09\u3068\u306f\u3001G \u3068\u540c\u3058\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u3092\u8868\u3059 DAG \u306e\u4e2d\u3067\u3001\u6700\u3082\u5c11\u306a\u3044\u8fba\u3092\u6301\u3064\u3082\u306e\u3067\u3042\u308b\u3002\u3053\u308c\u306f G \u306e\u30b5\u30d6\u30b0\u30e9\u30d5\u3067\u3042\u308a\u3001G \u304c u \u304b\u3089 v \u306b\u81f3\u308b\u3088\u308a\u9577\u3044\u30d1\u30b9\u3092\u6301\u3064\u5834\u5408\u306b\u8fba u \u2192 v \u3092\u5ec3\u68c4\u3059\u308b\u3053\u3068\u3067\u5f62\u6210\u3055\u308c\u308b\u3002\u63a8\u79fb\u9589\u5305\u3068\u540c\u69d8\u3001\u63a8\u79fb\u7c21\u7d04\u3082 DAG \u306b\u5bfe\u3057\u3066\u4e00\u610f\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u4e00\u65b9\u3001DAG \u4ee5\u5916\u306e\u6709\u5411\u30b0\u30e9\u30d5\u3067\u306f\u3001\u540c\u3058\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u3092\u6301\u3064\u6700\u5c0f\u90e8\u5206\u30b0\u30e9\u30d5\u304c\u8907\u6570\u5b58\u5728\u3059\u308b\u5834\u5408\u304c\u3042\u308b[15]\u3002  3\u8981\u7d20\u96c6\u5408\u306e\u90e8\u5206\u96c6\u5408\u9593\u306e\u96c6\u5408\u5305\u542b\uff08\u2286\uff09\u306e\u534a\u9806\u5e8f\u96c6\u5408\u3092\u8868\u3059\u30cf\u30c3\u30bb\u56f3DAG G \u304c\u534a\u9806\u5e8f \u2264 \u3067\u8868\u3055\u308c\u308b\u5230\u9054\u53ef\u80fd\u6027\u95a2\u4fc2\u3092\u6301\u3064\u3068\u304d\u3001G \u306e\u63a8\u79fb\u7c21\u7d04\u306f G \u30b5\u30d6\u30b0\u30e9\u30d5\u3067\u3042\u308a\u3001\u2264 \u306e\u88ab\u8986\u95a2\u4fc2\uff08\u82f1\u8a9e\u7248\uff09 \u306b\u3042\u308b\u5168\u3066\u306e\u30da\u30a2\u306b\u5bfe\u3057\u8fba u \u2192 v \u3092\u6301\u3064\u3002\u63a8\u79fb\u7c21\u7d04\u306f\u540c\u3058\u534a\u9806\u5e8f\u3092\u8868\u3059\u4ed6\u306e\u30b0\u30e9\u30d5\u306b\u6bd4\u3079\u3066\u8fba\u306e\u6570\u304c\u5c11\u306a\u304f\u3001\u30b0\u30e9\u30d5\u306e\u63cf\u753b\u304c\u5358\u7d14\u306b\u306a\u308b\u305f\u3081\u3001\u534a\u9806\u5e8f\u3092\u8996\u899a\u5316\u3059\u308b\u306e\u306b\u4fbf\u5229\u3067\u3042\u308b\u3002\u534a\u9806\u5e8f\u306e\u30cf\u30c3\u30bb\u56f3\u306f\u3001\u63a8\u79fb\u7c21\u7d04\u3092\u56f3\u793a\u3057\u305f\u3082\u306e\u3067\u3001\u5404\u8fba\u306e\u5411\u304d\u3092\u3001\u8fba\u306e\u59cb\u70b9\u306e\u9802\u70b9\u3092\u7d42\u70b9\u306e\u9802\u70b9\u3088\u308a\u3082\u4f4e\u3044\u4f4d\u7f6e\u306b\u7f6e\u3044\u3066\u793a\u3057\u3066\u3044\u308b[16]\u3002\u6ce8\u91c8\u30fb\u51fa\u5178[\u7de8\u96c6]^ Christofides, Nicos (1975), Graph theory: an algorithmic approach, Academic Press, pp.\u00a0170\u2013174, ISBN\u00a09780121743505\u00a0.^ Thulasiraman, K.; Swamy, M. N. S. (1992), \u201c5.7 Acyclic Directed Graphs\u201d, Graphs: Theory and Algorithms, John Wiley and Son, p.\u00a0118, ISBN\u00a0978-0-471-51356-8\u00a0.^ Bang-Jensen, J\u00f8rgen (2008), \u201c2.1 Acyclic Digraphs\u201d, Digraphs: Theory, Algorithms and Applications, Springer Monographs in Mathematics (2nd ed.), Springer-Verlag, pp.\u00a032\u201334, ISBN\u00a0978-1-84800-997-4\u00a0.^ \u201c\u4eee\u60f3\u901a\u8ca8\u306e\u672a\u6765\u306fDAG\u30b3\u30a4\u30f3\u306b\u3042\u308a\uff1f\u30d6\u30ed\u30c3\u30af\u30c1\u30a7\u30fc\u30f3\u306b\u4ee3\u308f\u308b\u6280\u8853\u306b\u6ce8\u76ee\u201d.   Cointelegraph. 2018\u5e741\u670829\u65e5\u95b2\u89a7\u3002^ \u201c\u30d6\u30ed\u30c3\u30af\u30c1\u30a7\u30fc\u30f3\u3067\u306f\u306a\u3044\u65b0\u6280\u8853\u30fbDAG\u3067\u69cb\u7bc9\u3055\u308c\u308b\u6697\u53f7\u901a\u8ca8\u3001Byteball\u3068\u306f\u3002\u305d\u306e\u30d3\u30b8\u30e7\u30f3\u306a\u3069\u3002\u201d.   Think Nomad. 2018\u5e741\u670829\u65e5\u95b2\u89a7\u3002^ \u201cDAG\u30d9\u30fc\u30b9\u306e\u6697\u53f7\u901a\u8ca8 Byteball\u3068\u306f\u3002\u201d.   Byteball\u306e\u672a\u6765. 2018\u5e741\u670829\u65e5\u95b2\u89a7\u3002^ \u201cByteball \u2014 smart payments made simple\u201d. 2018\u5e741\u670829\u65e5\u95b2\u89a7\u3002^ \u201c\u8a50\u6b3a\u547c\u3070\u308f\u308a\u3055\u308c\u305f\u3053\u3068\u3082\u3042\u3063\u305f\u304c\u3001\u6b21\u7b2c\u306b\u6ce8\u76ee\u5ea6\u3092\u5897\u3059\u7570\u8272\u306e\u8349\u30b3\u30a4\u30f3\u300cADK\u300d\u3068\u306f\uff1f\u201d. \u30cf\u30fc\u30d0\u30fc\u30d3\u30b8\u30cd\u30b9\u30aa\u30f3\u30e9\u30a4\u30f3. 2019\u5e746\u670830\u65e5\u95b2\u89a7\u3002^ Thulasiraman, K.; Swamy, M. N. S. (1992), \u201c5.7 Acyclic Directed Graphs\u201d, Graphs: Theory and Algorithms, John Wiley and Son, p.\u00a0118, ISBN\u00a0978-0-471-51356-8\u00a0.^ Bang-Jensen, J\u00f8rgen (2008), \u201c2.1 Acyclic Digraphs\u201d, Digraphs: Theory, Algorithms and Applications, Springer Monographs in Mathematics (2nd ed.), Springer-Verlag, pp.\u00a032\u201334, ISBN\u00a0978-1-84800-997-4\u00a0.^ Christofides, Nicos (1975), Graph theory: an algorithmic approach, Academic Press, pp.\u00a0170\u2013174\u00a0^ Mitrani, I. (1982), Simulation Techniques for Discrete Event Systems, Cambridge Computer Science Texts, 14, Cambridge University Press, p.\u00a027, ISBN\u00a09780521282826, https:\/\/books.google.com\/books?id=CF04AAAAIAAJ&pg=PA27\u00a0^ Kozen, Dexter (1992), The Design and Analysis of Algorithms, Monographs in Computer Science, Springer, p.\u00a09, ISBN\u00a0978-0-387-97687-7, https:\/\/books.google.com\/books?id=L_AMnf9UF9QC&pg=PA9\u00a0^ Banerjee, Utpal (1993), \u201cExercise 2(c)\u201d, Loop Transformations for Restructuring Compilers: The Foundations, Springer, p.\u00a019, Bibcode:\u00a01993ltfr.book…..B, ISBN\u00a0978-0-7923-9318-4, https:\/\/books.google.com\/books?id=Cog7zSSlqFwC&pg=PA19\u00a0^ Bang-Jensen, J\u00f8rgen; Gutin, Gregory Z. (2008), \u201c2.3 Transitive Digraphs, Transitive Closures and Reductions\u201d, Digraphs: Theory, Algorithms and Applications, Springer Monographs in Mathematics, Springer, pp.\u00a036\u201339, ISBN\u00a0978-1-84800-998-1, https:\/\/books.google.com\/books?id=4UY-ucucWucC&pg=PA36\u00a0^ Jungnickel, Dieter (2012), Graphs, Networks and Algorithms, Algorithms and Computation in Mathematics, 5, Springer, pp.\u00a092\u201393, ISBN\u00a0978-3-642-32278-5, https:\/\/books.google.com\/books?id=PrXxFHmchwcC&pg=PA92\u00a0.\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7041#breadcrumbitem","name":"\u6709\u5411\u975e\u5de1\u56de\u30b0\u30e9\u30d5 – Wikipedia"}}]}]