{"id":11174,"date":"2024-05-27T12:00:00","date_gmt":"2024-05-27T03:00:00","guid":{"rendered":"https:\/\/www.osakac.ac.jp\/whoslab\/?post_type=research&#038;p=11174"},"modified":"2024-11-25T11:01:30","modified_gmt":"2024-11-25T02:01:30","slug":"wakabayashi","status":"publish","type":"research","link":"https:\/\/www.osakac.ac.jp\/whoslab\/research\/wakabayashi\/","title":{"rendered":"<strong>\u591a\u91cd\u30bc\u30fc\u30bf\u5024\u306b\u95a2\u3059\u308b\u95a2\u4fc2\u5f0f\u3092\u63a2\u7a76\u3057\u3000<br>\u4e16\u7d00\u306e\u96e3\u554f\u300c\u30b6\u30ae\u30a8\u4e88\u60f3\u300d\u306b\u6311\u3080\uff01<\/strong>"},"content":{"rendered":"\n<p class=\"lead\">\u6570\u5b66\u306b\u306f\u300c\u25cb\u25cb\u4e88\u60f3\u300d\u3068\u547c\u3070\u308c\u308b\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002\u3042\u308b\u6570\u5b66\u8005\u304c\u300c\u307e\u3060\u8a3c\u660e\u306f\u3067\u304d\u3066\u3044\u306a\u3044\u3051\u308c\u3069\u3001\u304d\u3063\u3068\u3053\u3046\u306a\u308b\u306f\u305a\u3060\u300d\u3068\u7acb\u3066\u305f\u4eee\u8aac\u306e\u3053\u3068\u3067\u3001\u300c\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u300d\u3084\u300cP\u2260NP\u4e88\u60f3\u300d\u304c\u305d\u306e\u4ee3\u8868\u3067\u3059\u3002\u6570\u5b66\u306b\u306f\u3001\u3053\u3046\u3057\u305f\u672a\u89e3\u6c7a\u554f\u984c\u304c\u6570\u591a\u304f\u5b58\u5728\u3057\u3066\u3044\u307e\u3059\u3002<br>\u82e5\u6797\u51c6\u6559\u6388\u306f\u3001\u305d\u3093\u306a\u672a\u89e3\u6c7a\u554f\u984c\u306e\u3072\u3068\u3064\u3067\u3042\u308b\u300c\u30b6\u30ae\u30a8\u4e88\u60f3\u300d\u306b\u3064\u3044\u3066\u3001\uff12\u3064\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u304b\u3089\u53d6\u308a\u7d44\u3093\u3067\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong><strong>\u6570\u3092\u9650\u308a\u306a\u304f\u8db3\u3057\u3066\u3044\u304f\u3068\u3069\u3046\u306a\u308b\uff1f\u3000<\/strong><\/strong><br><strong>\u7121\u9650\u548c\u306b\u79d8\u3081\u3089\u308c\u305f\u8b0e\u306b\u6311\u3080\u6570\u5b66\u8005\u305f\u3061<\/strong><\/h2>\n\n\n\n<p><span data-tip=\"\u6b63\u306e\u6574\u6570\">\u81ea\u7136\u6570<\/span>\u306e\u7121\u9650\u548c\uff08\u9650\u308a\u306a\u304f\u8db3\u3057\u5408\u308f\u305b\u305f\u7d50\u679c\uff09\u306f\u7121\u9650\u5927\u306b\u306a\u308a\u307e\u3059\u3002\u3067\u306f\u3001\u81ea\u7136\u6570\u306e<span data-tip=\"\u305d\u306e\u6570\u306b\u304b\u3051\u5408\u308f\u305b\u308b\u30681\u306b\u306a\u308b\u6570\u3002ex\uff09\uff13\u306e\u9006\u6570\u306f1\/3\">\u9006\u6570<\/span>\u306e\u7121\u9650\u548c\u306f\uff1f \u3053\u308c\u3082\u7121\u9650\u5927\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"291\" src=\"https:\/\/www.osakac.ac.jp\/whoslab\/app\/uploads\/2024\/05\/wakabayashi.n_01-1024x291.png\" alt=\"\" class=\"wp-image-11188\"\/><\/figure>\n\n\n\n<p>\u3055\u3089\u306b\u3001\u81ea\u7136\u6570\u306e\u9006\u6570\u306e<span data-tip=\"\u540c\u3058\u6570\u3092\u4f55\u56de\u304b\u304b\u3051\u5408\u308f\u305b\u308b\u8a08\u7b97\u65b9\u6cd5\u3002\u300ca\u306en\u4e57\u300d\u3067\u8868\u3055\u308c\u308b\u6570an\u306e\u3053\u3068\u3092a\u306e\u3079\u304d\u4e57\u3068\u547c\u3076\">\u3079\u304d\u4e57<\/span>\u306e\u7121\u9650\u548c\u306f\u3069\u3046\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3082\u7121\u9650\u5927\u306b\u306a\u308b\u304b\u3068\u3044\u3046\u3068\u3001\u305d\u3046\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u9006\u6570\u306e\u3079\u304d\u4e57\u306e\u5834\u5408\u3001\u305d\u306e\u7121\u9650\u548c\u306f\u7121\u9650\u3067\u306f\u306a\u3044\u6570\u306b\u53ce\u675f\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001<span data-tip=\"\u30ec\u30aa\u30f3\u30cf\u30eb\u30c8\u30fb\u30aa\u30a4\u30e9\u30fc\uff081707~1783\uff09\u3002\u30b9\u30a4\u30b9\u51fa\u8eab\u306e\u6570\u5b66\u8005\u30fb\u5929\u4f53\u7269\u7406\u5b66\u8005\">\u6570\u5b66\u8005\u30aa\u30a4\u30e9\u30fc<\/span>\u306f1735\u5e74\u3001\u3053\u306e\u7121\u9650\u548c\u3092\u5186\u5468\u7387\u03c0\u3092\u4f7f\u3063\u3066\u975e\u5e38\u306b\u30b7\u30f3\u30d7\u30eb\u306b\u8a18\u8ff0\u3067\u304d\u308b\u3053\u3068\u3092\u767a\u898b\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"545\" src=\"https:\/\/www.osakac.ac.jp\/whoslab\/app\/uploads\/2024\/05\/wakabayashi.n_02-1024x545.png\" alt=\"\" class=\"wp-image-11189\"\/><\/figure>\n\n\n\n<p>300\u5e74\u8fd1\u304f\u3082\u524d\u306b\u3001\u624b\u8a08\u7b97\u3067\u4e0a\u8a18\u306e\u7f8e\u3057\u3044\u300c\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f\u300d\u304c\u5c0e\u304d\u51fa\u3055\u308c\u305f\u306e\u306f\u9a5a\u304f\u3079\u304d\u3053\u3068\u3067\u3059\u304c\u3001\u89e3\u660e\u3055\u308c\u305f\u306e\u306f\u5f0f\u3092\u898b\u3066\u308f\u304b\u308b\u901a\u308a\u5076\u6570\u4e57\u306e\u6642\u306e\u307f\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u305d\u306e\u5f8c\u3001<span data-tip=\"\u30b2\u30aa\u30eb\u30af\u30fb\u30d5\u30ea\u30fc\u30c9\u30ea\u30d2\u30fb\u30d9\u30eb\u30f3\u30cf\u30eb\u30c8\u30fb\u30ea\u30fc\u30de\u30f3\uff081826~1866\uff09\u3002\u30c9\u30a4\u30c4\u306e\u6570\u5b66\u8005\">\u6570\u5b66\u8005\u30ea\u30fc\u30de\u30f3<\/span>\u304c\u3001\u3053\u306e\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f\u3092\u30bc\u30fc\u30bf\u95a2\u6570\u3068\u3057\u3066\u8003\u6848\u3057\u3001\u3055\u3089\u306b<span data-tip=\"\u6574\u6570\u306e\u6bd4\uff1d\u5206\u6570\u3067\u8868\u305b\u306a\u3044\u6570\u306e\u3053\u3068\">\u7121\u7406\u6570<\/span>\u3092\u542b\u3080<span data-tip=\"\u6570\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u3059\u3079\u3066\u306e\u6570\u3002\u81ea\u7136\u6570\u30fb\u30bc\u30ed\u30fb\u8ca0\u306e\u6574\u6570\u30fb\u6709\u7406\u6570\u30fb\u7121\u7406\u6570\u7b49\u3001\u4e16\u306e\u4e2d\u306b\u5b9f\u5728\u3059\u308b\u6570\u306e\u3053\u3068\">\u5b9f\u6570<\/span>\u306b\u5e83\u3052\u3001\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u3068\u3057\u3066\u4e0b\u8a18\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"197\" src=\"https:\/\/www.osakac.ac.jp\/whoslab\/app\/uploads\/2024\/05\/wakabayashi.n_03-1024x197.png\" alt=\"\" class=\"wp-image-11190\"\/><\/figure>\n\n\n\n<p>\u305d\u3057\u3066\u3001\u3053\u306e\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u3092\u3001\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3092\u591a\u91cd\u30bc\u30fc\u30bf\u5024\u3068\u547c\u3073\u3001\u4ee5\u4e0b\u306e\u95a2\u6570\u3067\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"152\" src=\"https:\/\/www.osakac.ac.jp\/whoslab\/app\/uploads\/2024\/05\/wakabayashi.n_04-1024x152.png\" alt=\"\" class=\"wp-image-11192\"\/><figcaption class=\"wp-element-caption\">\u6b63\u6574\u6570\u00a0r\u00a0\u306b\u5bfe\u3057,\u6b63\u6574\u6570\u00a0r\u00a0\u500b\u306e\u7d44\u00a0k\u00a0= (k<sub>1<\/sub>, &#8230; ,\u00a0k<sub>r<\/sub>) \u3092\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u00a0\u3068\u547c\u3076.\u6700\u5f8c\u306e\u6210\u5206\u00a0k<sub>r<\/sub>\u00a0\u304c 2 \u4ee5\u4e0a\u3067\u3042\u308b\u5834\u5408\u3092\u8a31\u5bb9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u307e\u305f\u306f\u53ce\u675f\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u547c\u3076.\u307e\u305f,\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u00a0k\u00a0= (k<sub>1<\/sub>, &#8230; ,\u00a0k<sub>r<\/sub>) \u306e\u6210\u5206\u306e\u500b\u6570\u00a0r\u00a0\u3092\u00a0k\u00a0\u306e\u6df1\u3055\u00a0(depth),\u6210\u5206\u306e\u7dcf\u548c\u00a0k<sub>1<\/sub>\u00a0+ \u2026 +\u00a0k<sub>r<\/sub>\u00a0\u3092\u00a0k\u00a0\u306e\u91cd\u3055\u00a0(weight) \u3068\u547c\u3073,\u305d\u308c\u305e\u308c dep(k),wt(k) \u3068\u66f8\u304f.<\/figcaption><\/figure>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"block-9ec10696-52df-4467-8f07-2f5b79cdeae9\"><strong><strong>\u591a\u91cd\u30bc\u30fc\u30bf\u5024\u306e\u4e2d\u306b\u5fc5\u305a\u9375\u304c\u7720\u3063\u3066\u3044\u308b<\/strong>\u3000<strong><br>\uff12\u3064\u306e\u65b9\u5411\u304b\u3089\u95a2\u4fc2\u5f0f\u306e\u767a\u898b\u306b\u8feb\u308b<\/strong><\/strong><\/h2>\n\n\n\n<p>\u82e5\u6797\u51c6\u6559\u6388\u306f\u3001\u3053\u306e\u300c\u591a\u91cd\u30bc\u30fc\u30bf\u5024\u300d\u3092\u7814\u7a76\u3057\u3066\u3044\u307e\u3059\u3002\u591a\u91cd\u30bc\u30fc\u30bf\u5024\u306b\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u95a2\u4fc2\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3068\u4e88\u60f3\u3055\u308c\u3066\u304a\u308a\u3001\u6700\u3082\u6709\u540d\u306a\u306e\u306f1990\u5e74\u4ee3\u306b\u306f<span data-tip=\"\u30c9\u30f3\u30fb\u30d9\u30eb\u30ca\u30eb\u30c8\u30fb\u30b6\u30ae\u30a8\uff081951~\uff09\u3002\u6570\u8ad6\u3092\u5c02\u9580\u3068\u3059\u308b\u6570\u5b66\u8005\">\u6570\u5b66\u8005\u30b6\u30ae\u30a8<\/span>\u304c\u63d0\u5531\u3057\u305f\u6b21\u5143\u4e88\u60f3\u3067\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"958\" src=\"https:\/\/www.osakac.ac.jp\/whoslab\/app\/uploads\/2024\/05\/wakabayashi.n_04_1-1024x958.png\" alt=\"\" class=\"wp-image-11194\" style=\"width:833px;height:778px\"\/><figcaption class=\"wp-element-caption\">\u6574\u6570 k \u2265 2 \u306b\u5bfe\u3057,\u91cd\u3055 k \u306e\u4e0a\u754c\uff08\u8a31\u5bb9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u500b\u6570\uff09\u306f 2 ^{k \u2212 2} \u500b\u3068\u306a\u308b.\u91cd\u3055 3 \u306e\u8a31\u5bb9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f ( 3 ),( 1, 2 ) \u306e\uff12\u3064\uff0f\u6b21\u5143\u304c\u4e0a\u304c\u308b\u3054\u3068\u306b\u4e0a\u754c\u304c2\u4e57\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u76ee.<\/figcaption><\/figure>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u30b6\u30ae\u30a8\u4e88\u60f3\u306f\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u3088\u308a\u3082\u96e3\u554f\u3068\u3082\u3044\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u7c21\u5358\u306b\u3044\u3046\u3068\u3001\u305f\u3068\u3048\u3070\u4e0a\u8a18\u3067\u91cd\u305512\u306e\u8a31\u5bb9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f1024\u500b\u3067\u3059\u304c\u3001\u672c\u8cea\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u3082\u306e\u306f12\u3057\u304b\u306a\u3044\u306f\u305a\u3060\u3068\u3044\u3046\u4e88\u60f3\u3067\u3059\u3002\u305d\u306e\u610f\u5473\u306e\u3042\u308b\u3082\u306e\u3092\u3042\u3076\u308a\u51fa\u3059\u305f\u3081\u306e\u95a2\u4fc2\u5f0f\u306e\u767a\u898b\u306b\u5411\u3051\u3066\u3001\u65e5\u3005\u7814\u7a76\u3092\u7d9a\u3051\u3066\u3044\u308b\u306e\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305f\u540c\u6642\u306b\u3001\u82e5\u6797\u51c6\u6559\u6388\u306f\u591a\u91cd\u30bc\u30fc\u30bf\u5024\u306b\u5bfe\u3057\u3001\u7570\u306a\u308b\u9762\u304b\u3089\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3082\u884c\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u308c\u304c\u3001\u6839\u4ed8\u304d\u6728\u5199\u50cf\u3068\u547c\u3070\u308c\u308b\u30b0\u30e9\u30d5\u3092\u4f7f\u3063\u305f\u65b9\u6cd5\u3067\u3059\u3002\u30b3\u30f3\u30cc\u2010\u30af\u30e9\u30a4\u30de\u30fc\u306b\u3088\u308b\u6839\u4ed8\u304d\u6728\u306e\u30db\u30c3\u30d7\u4ee3\u6570\u304c\u3001<span 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