{"id":651,"date":"2018-07-03T12:00:09","date_gmt":"2018-07-03T03:00:09","guid":{"rendered":"http:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=651"},"modified":"2018-07-03T12:00:09","modified_gmt":"2018-07-03T03:00:09","slug":"sat-%e5%85%85%e8%b6%b3%e5%8f%af%e8%83%bd%e6%80%a7%e5%95%8f%e9%a1%8c%e3%81%ae%e3%82%a4%e3%82%b8%e3%83%b3%e3%82%b0%e8%a1%a8%e7%8f%be-by-%e5%b0%8f%e6%9e%97","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/07\/03\/sat-%e5%85%85%e8%b6%b3%e5%8f%af%e8%83%bd%e6%80%a7%e5%95%8f%e9%a1%8c%e3%81%ae%e3%82%a4%e3%82%b8%e3%83%b3%e3%82%b0%e8%a1%a8%e7%8f%be-by-%e5%b0%8f%e6%9e%97\/","title":{"rendered":"\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT)\u306eQUBO\u8868\u73fe -\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c\u306b\u5e30\u7740\u3055\u305b\u308b\u65b9\u6cd5-"},"content":{"rendered":"\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001Karp\u306e21\u306eNP\u5b8c\u5168\u554f\u984c\u306e\u4e00\u3064\u3067\u3042\u308b \u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT; satisfiability problem)\u306b\u95a2\u3057\u3066\u3001\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c (MIS; maximum independent set)\u306b\u5e30\u7740\u3057\u3066\u3001\u554f\u984c\u3092QUBO\u8868\u73fe\u306b\u5909\u63db\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3059\u308b\u3002\u672c\u8a18\u4e8b\u4f5c\u6210\u306b\u3042\u305f\u3063\u3066\u306f\u3001<a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=43\">\u300c\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u306e\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u8868\u73fe &#8220;Ising formulations of many NP problems&#8221; by Andrew Lucas (2014)\u300d<\/a>\u3067\u7d39\u4ecb\u3057\u305f\u8ad6\u6587\u3092\u53c2\u8003\u306b\u3057\u305f\u3002<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/07\/03\/sat-%e5%85%85%e8%b6%b3%e5%8f%af%e8%83%bd%e6%80%a7%e5%95%8f%e9%a1%8c%e3%81%ae%e3%82%a4%e3%82%b8%e3%83%b3%e3%82%b0%e8%a1%a8%e7%8f%be-by-%e5%b0%8f%e6%9e%97\/#%E5%85%85%E8%B6%B3%E5%8F%AF%E8%83%BD%E6%80%A7%E5%95%8F%E9%A1%8C_%E3%81%A8%E3%81%AF\" >\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c \u3068\u306f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/07\/03\/sat-%e5%85%85%e8%b6%b3%e5%8f%af%e8%83%bd%e6%80%a7%e5%95%8f%e9%a1%8c%e3%81%ae%e3%82%a4%e3%82%b8%e3%83%b3%e3%82%b0%e8%a1%a8%e7%8f%be-by-%e5%b0%8f%e6%9e%97\/#SAT%E3%81%AEMIS%E3%81%B8%E3%81%AE%E5%A4%89%E6%8F%9B%E3%82%92%E7%94%A8%E3%81%84%E3%81%9FQUBO%E8%A1%A8%E7%8F%BE\" >SAT\u306eMIS\u3078\u306e\u5909\u63db\u3092\u7528\u3044\u305fQUBO\u8868\u73fe<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/07\/03\/sat-%e5%85%85%e8%b6%b3%e5%8f%af%e8%83%bd%e6%80%a7%e5%95%8f%e9%a1%8c%e3%81%ae%e3%82%a4%e3%82%b8%e3%83%b3%e3%82%b0%e8%a1%a8%e7%8f%be-by-%e5%b0%8f%e6%9e%97\/#%E3%81%BE%E3%81%A8%E3%82%81\" >\u307e\u3068\u3081<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%85%85%E8%B6%B3%E5%8F%AF%E8%83%BD%E6%80%A7%E5%95%8F%E9%A1%8C_%E3%81%A8%E3%81%AF\"><\/span>\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c \u3068\u306f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT)\u3068\u306f\u3001\u771f\u507d\u5024\u3092\u3068\u308b\u3044\u304f\u3064\u304b\u306e\u5909\u6570\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u305f\u547d\u984c\u8ad6\u7406\u5f0f\u306b\u5bfe\u3057\u3066\u3001\u5909\u6570\u306e\u5024\u3092\u3046\u307e\u304f\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u305d\u306e\u5024\u3092\u771f\uff08True\uff09\u306b\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\u3059\u308b\u554f\u984c\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u6b21\u306e\u4f8b\u3067\u306f$x_1 = \\text{True},x_2= \\text{True}$\u3068\u3059\u308b\u3053\u3068\u3067\u8ad6\u7406\u5f0f\u306fTrue\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<p>$$\n{\\psi = (x_1 \\lor x_4 \\lor \\overline{x_3} \\lor x_6)\\land(x_5 \\lor x_2)\\land(\\overline{x_1} \\lor x_3 \\lor x_2)}\n$$<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u7528\u8a9e\u3092\u7528\u3044\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8ad6\u7406\u5f0f$\\psi$\u3092\u69cb\u6210\u3059\u308b\u5909\u6570$x$\u3068\u305d\u306e\u5426\u5b9a$\\overline{x}$\u3092\u307e\u3068\u3081\u3066<strong>\u30ea\u30c6\u30e9\u30eb<\/strong>\u3068\u3044\u3046\u3002<\/li>\n\n\n\n<li>\u62ec\u5f27\u5185\u90e8\u306e\u3088\u3046\u306b\u3001\u30ea\u30c6\u30e9\u30eb\u306e\u8ad6\u7406\u548c\u306e\u307f\u3067\u69cb\u6210\u3055\u308c\u308b\u90e8\u5206\u3092<strong>\u7bc0<\/strong>\u3068\u3044\u3046\u3002<\/li>\n\n\n\n<li>\u8ad6\u7406\u5f0f\u304c\u7bc0\u306e\u8ad6\u7406\u7a4d\u3067\u69cb\u6210\u3055\u308c\u308b\u5834\u5408\u3092<strong>CNF-SAT<\/strong>\u3068\u3044\u3046\u3002\u3069\u3093\u306a\u5f62\u306e\u8ad6\u7406\u5f0f\u3082\u30c9\u30fb\u30e2\u30eb\u30ac\u30f3\u306e\u6cd5\u5247\u3084\u5206\u914d\u6cd5\u5247\u306a\u3069\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u5fc5\u305a\u3053\u306e\u5f62\u306b\u5e30\u7740\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li>CNF-SAT\u306e\u3046\u3061\u3001\u7279\u306b\u3069\u306e\u7bc0\u3092\u69cb\u6210\u3059\u308b\u30ea\u30c6\u30e9\u30eb\u6570\u3082\u305f\u304c\u3060\u304bk\u500b\u3068\u306a\u3063\u3066\u3044\u308b\u3082\u306e\u3092<strong>$k$-SAT<\/strong>\u3068\u3044\u3046\u3002<\/li>\n<\/ul>\n\n\n\n<p>$k \\geq 3$\u306a\u308b$k$-SAT\u306fNP\u5b8c\u5168\u554f\u984c\u3067\u3042\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u304a\u308a\u3001\u3053\u308c\u3092\u591a\u9805\u5f0f\u6642\u9593\u3067\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u77e5\u3089\u308c\u3066\u3044\u306a\u3044\u3002SAT\u306f\u521d\u3081\u3066NP\u5b8c\u5168\u3067\u3042\u308b\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u305f (Cook-Levin\u306e\u5b9a\u7406; <a href=\"https:\/\/www.cs.toronto.edu\/~sacook\/homepage\/1971.pdf\">Cook (1971)<\/a>) \u6b74\u53f2\u7684\u306b\u3082\u91cd\u8981\u306a\u554f\u984c\u3067\u3042\u308a\u3001\u73fe\u5728\u3067\u3082\u30b7\u30b9\u30c6\u30e0\u691c\u8a3c\u3001\u5236\u7d04\u5145\u8db3\u554f\u984c (CSP)\u3001\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u3001\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u306a\u3069\u591a\u69d8\u306a\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306e\u5171\u901a\u8a00\u8a9e\u3068\u3057\u3066\u306e\u610f\u5473\u304c\u3042\u308b\u3002\u73fe\u5728\u5e83\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u308bSAT\u30bd\u30eb\u30d0\u30fc\u306fDPDL\u3084CDCL\u3068\u3044\u3063\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u30d9\u30fc\u30b9\u3068\u3057\u3066\u304a\u308a\u3001\u6570\u767e\u4e07\u3082\u306e\u5909\u6570\u3092\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u30c4\u30fc\u30eb\u3068\u3057\u3066\u767a\u5c55\u3092\u9042\u3052\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p>\u4e00\u65b9\u3001\u30a4\u30b8\u30f3\u30b0\u30fbQUBO\u8868\u73fe\u3092\u7528\u3044\u305f\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30c3\u30af\u89e3\u6cd5\u3068\u3057\u3066\u306f\u8ad6\u7406\u7a4d\u3092\u5f37\u78c1\u6027\u76f8\u4e92\u4f5c\u7528\u3001\u8ad6\u7406\u548c\u3092\u5f37\u78c1\u6027\u76f8\u4e92\u4f5c\u7528\u3068\u5c40\u6240\u78c1\u5834\u3067\u81ea\u7136\u306b\u8868\u73fe\u3057\u305f\u3082\u306e\u304c\u8003\u3048\u3089\u308c\u308b\u304c\u30013-SAT\u3067\u306f3\u4f53\u76f8\u4e92\u4f5c\u7528\u3092\u6271\u3046\u5fc5\u8981\u304c\u3042\u308b\u3002D-Wave\u30de\u30b7\u30f3\u3067\u306f2\u4f53\u306e\u76f8\u4e92\u4f5c\u7528\u307e\u3067\u3057\u304b\u30cd\u30a4\u30c6\u30a3\u30d6\u306b\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u305f\u3081\u30011\u3064\u306e\u88dc\u52a9\u91cf\u5b50\u30d3\u30c3\u30c8\u3092\u52a0\u3048\u30663\u4f53\u30922\u4f53\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u4e3b\u306b\u7528\u3044\u3089\u308c\u308b\u3002<br>\u2192 \u53c2\u8003\u8a18\u4e8b\uff08\u5916\u90e8\u30b5\u30a4\u30c8\uff09\u300c<a href=\"https:\/\/quantum.fixstars.com\/introduction_to_quantum_computer\/quantum_annealing\/programming\/conversion\/\" target=\"_blank\" rel=\"noopener\">\u30a4\u30b8\u30f3\u30b0\u6a21\u578b\u3078\u306e\u5909\u63db\uff08\u682a\u5f0f\u4f1a\u793e\u30d5\u30a3\u30c3\u30af\u30b9\u30bf\u30fc\u30ba\uff09<\/a>\u300d<\/p>\n\n\n\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u5225\u89e3\u6cd5\u3068\u3057\u3066\u30012\u4f53\u306e\u76f8\u4e92\u4f5c\u7528\u3060\u3051\u3067\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304c\u8a18\u8ff0\u53ef\u80fd\u306a\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c\u306b\u5e30\u7740\u3059\u308b\u3053\u3068\u30673-SAT\u554f\u984c\u3092\u89e3\u304f\u65b9\u6cd5\u306b\u3064\u3044\u3066\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6700\u5927\u72ec\u7acb\u96c6\u5408 (MIS)\u3068\u306f<\/h3>\n\n\n\n<p>\u307e\u305a\u72ec\u7acb\u96c6\u5408\uff08independent set\uff09\u306b\u3064\u3044\u3066\u8aac\u660e\u3059\u308b\u3002\u72ec\u7acb\u96c6\u5408$V&#8217;$\u3068\u306f\u3001\u3042\u308b\u30b0\u30e9\u30d5$G(V,E)$($V$\u306f\u9802\u70b9\u3001$E$\u306f\u8fba\u306e\u96c6\u5408)\u304c\u4e0e\u3048\u3089\u308c\u305f\u6642\u306b\u3001\u9802\u70b9\u306e\u306a\u304b\u3067\u4e92\u3044\u306b\u8fba\u3092\u5171\u6709\u3057\u3066\u3044\u306a\u3044\u3088\u3046\u306a\u3082\u306e\u3092\u8981\u7d20\u306b\u3082\u3064\u3001V\u306e\u90e8\u5206\u96c6\u5408\u3067\u3042\u308b\u3002\u3053\u3053\u3067\u3001\u30b0\u30e9\u30d5$G$\u306b\u304a\u3044\u3066\u6700\u3082\u5927\u304d\u306a\u72ec\u7acb\u96c6\u5408\u3092MIS\u3068\u3044\u3044\u3001\u305d\u306e\u5927\u304d\u3055\u3092$\\alpha(G)(= \\max |V&#8217;|)$\u3067\u8868\u3059\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u6b21\u306e\u30b0\u30e9\u30d5\u3067\u306f\u3001\u8272\u306e\u3064\u3044\u305f\u9802\u70b9\u306e\u96c6\u5408\u304cMIS\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image wp-image-758 size-full\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/sat_graph1.png\" alt=\"\u6700\u5927\u72ec\u7acb\u96c6\u5408\u306e\u4f8b\" class=\"wp-image-758\"\/><figcaption class=\"wp-element-caption\">\u6700\u5927\u72ec\u7acb\u96c6\u5408\u306e\u4f8b<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"SAT%E3%81%AEMIS%E3%81%B8%E3%81%AE%E5%A4%89%E6%8F%9B%E3%82%92%E7%94%A8%E3%81%84%E3%81%9FQUBO%E8%A1%A8%E7%8F%BE\"><\/span>SAT\u306eMIS\u3078\u306e\u5909\u63db\u3092\u7528\u3044\u305fQUBO\u8868\u73fe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u5927\u304d\u306a\u6d41\u308c\u3068\u3057\u3066\u306f\u3001<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>SAT\u306e\u8ad6\u7406\u5f0f\u3092\u5bfe\u5fdc\u3059\u308b\u30b0\u30e9\u30d5\u306b\u5909\u63db \u2192 \u5909\u63db\u3057\u305f\u30b0\u30e9\u30d5\u306eMIS\u554f\u984c\u3092QUBO\u8868\u73fe\u306b\u5b9a\u5f0f\u5316<\/strong><\/p>\n\n\n\n<p>\u306e\u3088\u3046\u306b\u306a\u308b\u3002\u307e\u305fQUBO\u3092\u4f5c\u6210\u3059\u308b\u4e0a\u3067\u3001MIS\u554f\u984c\u304c\u6700\u5c0f\u88ab\u8986\u554f\u984c\u3084\u3001\u88dc\u30b0\u30e9\u30d5\u306b\u5bfe\u3059\u308b\u6700\u5927\u30af\u30ea\u30fc\u30af\u554f\u984c\u3068\u7b49\u4fa1\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u76ee\u3057\u3066\u5b9a\u5f0f\u5316\u3059\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3-SAT\u306e\u30b0\u30e9\u30d5\u3078\u306e\u5909\u63db\u4f8b<\/h3>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u7bc0\u65702\u3067\u3001\u72ed\u7fa9\u306e3-SAT\uff08\u3069\u306e\u7bc0\u3082\u30ea\u30c6\u30e9\u30eb\u6570\u304c\u3061\u3087\u3046\u30693\u500b\uff09\u3067\u306e\u5834\u5408\u3092\u8003\u3048\u308b\u3002\u307e\u305a\u8ad6\u7406\u5f0f$\\psi \uff1d\uff08x_1 \\lor x_2 \\lor \\overline{x_3})\\land(\\overline{x_1} \\lor x_3 \\lor x_2)$\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u3057\u3066\u3001\u5bfe\u5fdc\u3059\u308b\u30b0\u30e9\u30d5$G(V,E)$\u3092\u4ee5\u4e0b\u306e\u624b\u9806\u306b\u5f93\u3063\u3066\u4f5c\u6210\u3057\u3066\u3044\u304f\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8ad6\u7406\u5f0f\u53f3\u8fba\u306e\u7bc0\u3092\u3001\u5de6\u304b\u3089\u7bc0$c_1,c_2(c \\in C)$\u3068\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u7bc0$c_i$\u4e2d\u306e3\u5909\u6570\u3092\u3001\u5de6\u304b\u3089\u9802\u70b9$v_{i,1},v_{i,2},v_{i,3}(v \\in V)$\u306b\u5bfe\u5fdc\u3065\u3051\u3066\u3001\u9802\u70b9\u3092\u66f8\u304f\u3002<\/li>\n\n\n\n<li>\u5404\u7bc0\u3068\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u306e\u90e8\u5206\u96c6\u5408\u306b\u3064\u3044\u3066\u3001\u8981\u7d20\u306e\u9802\u70b9\u540c\u58eb\u3092\u8fba\u3067\u7d50\u3076\u3002\uff08\u3053\u306e\u3068\u304d\u56f3\u306e\u4e09\u89d2\u5f62\u3092\u5f62\u6210\u3059\u308b\uff09<\/li>\n\n\n\n<li>\u3042\u308b\u5909\u6570$x$\u3068\u305d\u306e\u5426\u5b9a$\\overline{x}$\u306b\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u540c\u58eb\u3092\u8fba\u3067\u7d50\u3076\u3002\uff08\u4e09\u89d2\u5f62\u540c\u58eb\u306e\u9023\u7d50\u306b\u76f8\u5f53\uff09<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/sat_graph2.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/sat_graph2.png\" alt=\"2\u7bc0\u304b\u3089\u306a\u308b3-SAT\u554f\u984c\u306e\u30b0\u30e9\u30d5\u5316\" class=\"wp-image-764\"\/><\/a><figcaption class=\"wp-element-caption\">2\u7bc0\u304b\u3089\u306a\u308b3-SAT\u554f\u984c\u306e\u30b0\u30e9\u30d5\u5316<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\">\u30b0\u30e9\u30d5\u306eMIS\u3092\u6c42\u3081\u308b\u3053\u3068\u306fSAT\u3092\u89e3\u304f\u3053\u3068\u3068\u7b49\u4fa1<\/h3>\n\n\n\n<p>\u4ee5\u4e0a\u306e\u3088\u3046\u306b\u4f5c\u3063\u305f\u30b0\u30e9\u30d5\u306eMIS\u306b\u95a2\u3057\u3066\u3001\u6b21\u306e\u9a5a\u304f\u3079\u304d\u4e8b\u5b9f\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u3002\u305d\u308c\u306f\u3001<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>\u30b0\u30e9\u30d5\u306eMIS\u306e\u8981\u7d20\u6570\u304c\u5143\u306eSAT\u306e\u7bc0\u6570\u3068\u7b49\u3057\u3044\u6642\u3001SAT\u306e\u8ad6\u7406\u5f0f\u306fTrue\u3068\u306a\u308b<\/strong><\/p>\n\n\n\n<p>\u3064\u307e\u308a\u3001\u5f0f\u3067\u8868\u305b\u3070\u3001<\/p>\n\n\n\n<p>$$\n{\\alpha(G) = |C| \\Leftrightarrow \\psi =&nbsp;True}\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u306a\u305c\u3053\u306e\u3088\u3046\u306b\u306a\u308b\u304b\u3092\u8aac\u660e\u3059\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">$\\alpha(G)=|C| \\Rightarrow \\psi = \\text{True} $ \u306e\u8aac\u660e<\/h4>\n\n\n<div class=\"wp-block-image wp-image-765 size-full\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/sat_graph3.png\" alt=\"\u5909\u63db\u5148\u306e\u30b0\u30e9\u30d5\u306e\u6700\u5927\u72ec\u7acb\u96c6\u5408\" class=\"wp-image-765\"\/><figcaption class=\"wp-element-caption\">\u5909\u63db\u5148\u306e\u30b0\u30e9\u30d5\u306e\u6700\u5927\u72ec\u7acb\u96c6\u5408<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u4f8b\u3048\u3070$v_{1,2}$\u3068$v_{2,1}$\u3092\u72ec\u7acb\u96c6\u5408\u306b\u542b\u3081\u308b\u3068\u3059\u308b\u3068\u3001\u7bc0\u306b\u6ce8\u76ee\u3057\u3066\u307f\u308c\u3070$\\alpha(G) \\leq |C|(=2)$\u306f\u5fc5\u305a\u6210\u7acb\u3059\u308b\u306e\u3067\uff08\u5404\u7bc0\u306b\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u306e\u90e8\u5206\u96c6\u5408\u304b\u3089\u306f\u3001\u305f\u304b\u3060\u304b\u4e00\u3064\u307e\u3067\u3057\u304b\u72ec\u7acb\u96c6\u5408\u306e\u8981\u7d20\u3092\u3068\u308a\u3048\u306a\u3044\uff09\u3001\u3053\u308c\u306fMIS\u3068\u306a\u3063\u3066\u3044\u3066\u3001\u5de6\u5074\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001MIS\u306b\u3068\u3063\u305f\u9802\u70b9\u306b\u5bfe\u5fdc\u3059\u308b\u5909\u6570x\u306b1\u3092\u4ee3\u5165\u3057\u3066($v_{12} \\rightarrow x_{2} = 1,v_{21} \\rightarrow \\overline{x}_{1} = 1$\uff09\u3001$\\psi$\u3092\u78ba\u8a8d\u3057\u3066\u307f\u308b\u3068<\/p>\n\n\n\n<p>$$\n{\\psi=(0 \\lor 1 \\lor \\overline{x_3})\\land(1 \\lor x_3 \\lor 1)}\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u3063\u3066\u304a\u308a\u3001\u3053\u308c\u306f$x_3$\u306e\u5024\u306b\u95a2\u308f\u3089\u305aTrue\u3068\u306a\u308b\u3002\u306a\u305c\u306a\u3089\u3070\u3001$\\psi$\u304cTrue\u3068\u306a\u308b\u3068\u304d\u306f\u5404\u7bc0\u3067\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306e\u30ea\u30c6\u30e9\u30eb\u304cTrue\u3067\u3042\u308c\u3070\u3088\u3044\u304b\u3089\u3060\u3002\u307e\u305f\u4e0a\u8ff0\u306e\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u304a\u3051\u308b\u624b\u98064\u3067\u306e\u64cd\u4f5c\u306b\u3088\u308a\u3001$x$\u3068$\\overline{x}$\u304c\u540c\u6642\u306b1\u306b\u306a\u308b\u3088\u3046\u306a\u77db\u76fe\u306f\u8d77\u3053\u3089\u306a\u3044\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b\u3002\u3053\u306e\u3088\u3046\u306b\u8003\u3048\u308b\u3068\u3001\u5404\u7bc0\u306b\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u306e\u90e8\u5206\u96c6\u5408\u304b\u3089\u9802\u70b9\u3092\u4e00\u3064\u72ec\u7acb\u96c6\u5408\u306b\u6301\u3063\u3066\u3053\u308c\u308b\u3068\u304d\u3001\u5404\u7bc0\u3067\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306e\u30ea\u30c6\u30e9\u30eb\u3092True\u306b\u3067\u304d\u308b\u3053\u3068\u3068\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">$\\alpha(G)=|C| \\Leftarrow \\psi=\\text{True} $ \u306e\u8aac\u660e<\/h4>\n\n\n\n<p>\u4eca\u5ea6\u306f\u9069\u5f53\u306b$x_1=1,x_2=1,x_3=1$\u3068\u306a\u3063\u3066\u3044\u308b\u5834\u5408\u3092\u8003\u3048\u3088\u3046\u3002<\/p>\n\n\n\n<p>$$\n{\\psi =\uff081 \\lor 1 \\lor 0)\\land(0 \\lor 1 \\lor 1)=True}\n$$<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/sat_graph4.png\" alt=\"\" class=\"wp-image-766\"\/><\/figure>\n<\/div>\n\n\n<p>\u3053\u308c\u306f\u53f3\u5074\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u3053\u3053\u3067\u5404\u7bc0\u304b\u3089x=1\u3068\u306a\u3063\u3066\u3044\u308b\u3082\u306e\u3068\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u3092\u9069\u5f53\u306b\u4e00\u3064\u305a\u3064\u9078\u3076\u3002\u4f8b\u3048\u3070$v_{11},v_{23}$\u3068\u3057\u3088\u3046\u3002\u3053\u306e\u3068\u304d\u5404\u7bc0\u304b\u3089\u4e00\u3064\u305a\u3064\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u3092\u9078\u3093\u3067\u3044\u308b\u306e\u3067\u3001\u5f53\u7136\u3053\u308c\u3089\u306e\u9802\u70b9\u306f\u7bc0\u306e\u6570\u3060\u3051\u5b58\u5728\u3057\u3001$x=1$ \u3067\u3042\u308c\u3070\u5fc5\u305a$\\overline{x}=0$\u3068\u306a\u308b\u3088\u3046\u306a\u8ad6\u7406\u7684\u306a\u5bfe\u5fdc\u304c\u767a\u751f\u3059\u308b\u306e\u3067\u9078\u3093\u3060\u9802\u70b9\u306f\u8fba\u3067\u7d50\u3070\u308c\u3066\u3044\u308b\u3053\u3068\u306f\u306a\u304f\u3001\u5fc5\u305a\u72ec\u7acb\u96c6\u5408\u306e\u8981\u7d20\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u306a\u304a\u304b\u3064MIS\u3068\u3082\u306a\u3063\u3066\u3044\u308b\u3002<br><br>\u3053\u306e\u3088\u3046\u306b\u8003\u3048\u308b\u3068\u3001$\\psi$\u304cTrue\u306b\u306a\u3063\u3066\u3044\u308b\u6642\u70b9\u3067\u5404\u7bc0\u304b\u3089\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306e\u9802\u70b9\u3092\u9078\u3093\u3067\u3001MIS\u306e\u5f62\u6210\u304c\u53ef\u80fd\u306a\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">$k$-SAT\u306e\u5834\u5408<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u5b9a\u7fa9<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30ea\u30c6\u30e9\u30eb: $L = \\{x_1,x_2,&#8230;,x_n,\\overline{x_1},\\overline{x_2},&#8230;,\\overline{x_n}\\}, x \\in {0,1}$<\/li>\n\n\n\n<li>\u9802\u70b9: $v_i \\in V, v_i$\u306b\u5bfe\u5fdc\u3059\u308b\u5909\u6570$y_i \\in &nbsp;L, 1 \\leq i \\leq n$\u3001\u7279\u306b\u7bc0$c_p$\u306e\u5de6\u304b\u3089q\u756a\u76ee\u306ey\u3068\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u306f$v_{p,q} = v_{3(p-1)+q}\\ \\ \\ (v_1 = v_{1,1},v_2 = v_{1,2},v_3 = v_{1,3},v_4 = v_{2,1},&#8230;,v_n = v_{m,k(m)})$<\/li>\n\n\n\n<li>\u7bc0: $c_i = v_{i,1} \\lor v_{i,2} \\lor &#8230; \\lor v_{i,k},1 \\leq i \\leq m,1 \\leq k(i)\\\\$<\/li>\n\n\n\n<li>\u8ad6\u7406\u5f0f: $\\psi = c_1 \\land c_2 \\land &#8230; \\land c_m\\\\$<\/li>\n\n\n\n<li>\u72ec\u7acb\u96c6\u5408: $V&#8217; \\subseteq V$<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u30b0\u30e9\u30d5\u4f5c\u6210\u306e\u624b\u9806<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5404\u9802\u70b9v\u304c\u3068\u308b\u5909\u6570x\u3092\u5bfe\u5fdc\u3055\u305b\u305f\u30b0\u30e9\u30d5G\u3092\u63cf\u304f\u3002<\/li>\n\n\n\n<li>\u5404\u7bc0\u306b\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u306e\u90e8\u5206\u96c6\u5408\u306b\u5c5e\u3059\u308bv\u540c\u58eb\u3092\u8fba\u3067\u7e4b\u3050\u3002<\/li>\n\n\n\n<li>$y_{p,q} = \\overline{y_{p,q}}$\u3068\u306a\u308b\u3088\u3046\u306av\u540c\u58eb\u3092\u8fba\u3067\u7e4b\u3050\u3002<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/sat_graph5.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/sat_graph5.png\" alt=\"\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c \u306e\u30b0\u30e9\u30d5\u5316\" class=\"wp-image-767\"\/><\/a><figcaption class=\"wp-element-caption\">\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c \u306e\u30b0\u30e9\u30d5\u5316<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u4ee5\u4e0a\u306e\u624b\u9806\u306b\u3088\u308a\u3001\u4e0a\u56f3\u306e\u3088\u3046\u306a\u6b63\u591a\u89d2\u5f62\u306e\u9802\u70b9\u3092\u6301\u3064\u5b8c\u5168\u30b0\u30e9\u30d5\u540c\u58eb\u304c\u7e4b\u304c\u3063\u305f\u3088\u3046\u306a\u30a4\u30e1\u30fc\u30b8\u3067\u8ad6\u7406\u5f0f\u306b\u5bfe\u5fdc\u3059\u308b\u30b0\u30e9\u30d5$G(V,E)$\u306f\u5b8c\u6210\u3059\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u5b9a\u5f0f\u5316<\/h4>\n\n\n\n<p>\u3053\u3053\u3067\u4f5c\u6210\u3057\u305f\u30b0\u30e9\u30d5$G(V,E)$\u306b\u5bfe\u3057MIS\u554f\u984c\u3092\u8003\u3048\u308b\u306e\u3060\u304c\u3001\u524d\u8ff0\u3057\u305f\u3088\u3046\u306b\u3053\u306e\u88dc\u30b0\u30e9\u30d5\u306b\u5bfe\u3059\u308b\u6700\u5927\u30af\u30ea\u30fc\u30af\u554f\u984c\u3092\u8003\u3048\u308b\u3068\u3001<br>\/T-Wave\/?p=97<br>\u3053\u306e\u89e3\u8aac\u306e\u3088\u3046\u306a\u5b9a\u5f0f\u5316\u304c\u53ef\u80fd\u3067\u3042\u308b\u3002\u3059\u306a\u308f\u3061\u6b21\u306e\u3088\u3046\u3002<\/p>\n\n\n\n<p>\n    $$\n    y_i =\n    \\begin{cases}\n    1 &amp; (if \\hspace{5pt} v_i \\in V&#8217;)\\\\\n    0 &amp; (otherwise)\n    \\end{cases}\n    $$\n<\/p>\n\n\n\n<p>$$\n\\mathrm{Obj}(\\mathbf{y}) = -A \\sum^n_{i=1}y_i + B \\sum_{\\{v_i,v_j\\} \\in E}y_i y_j\n$$<\/p>\n\n\n\n<p>\u5b9f\u88c5\u306f\u6975\u3081\u3066\u30b7\u30f3\u30d7\u30eb\u3067\u3001\u72ec\u7acb\u96c6\u5408\u306b\u542b\u307e\u308c\u308b\u9802\u70b9\u6570\u304c\u591a\u3044\u307b\u3069\u76ee\u7684\u95a2\u6570\u306f\u5c0f\u3055\u304f\u306a\u308a\u3001\u8fba\u3067\u7d50\u3070\u308c\u3066\u3044\u308b\u3088\u3046\u306a\u4e8c\u3064\u306e\u9802\u70b9\u3092\u540c\u6642\u306b\u72ec\u7acb\u96c6\u5408\u3078\u542b\u3081\u3088\u3046\u3068\u3057\u305f\u6642\u306b\u76ee\u7684\u95a2\u6570\u304c\u5927\u304d\u304f\u306a\u308b\u7f70\u91d1\u9805\u3092\u3082\u3064\uff08$\\{v_i,v_j\\}$\u306f\u3053\u306e2\u9802\u70b9\u3092\u3064\u306a\u3050\u8fba\u3092\u8868\u3059\uff09\u3002\u3053\u3053\u3067\u306f\u9802\u70b9\u306b\u91cd\u307f\u3092\u8003\u3048\u306a\u3044\u306e\u3067\u6b63\u306e\u5b9a\u6570$A, B$\u3067\u8003\u3048\u308c\u3070\u826f\u3044\u3002<br>\u4ee5\u4e0a\u306b\u304a\u3044\u3066MIS\u306e\u5927\u304d\u3055\u3092\u6c42\u3081\u305f\u6642\u3001$\\alpha(G) = m$\u3068\u306a\u308b\u3088\u3046\u306a$x$\u306e\u7d44\u307f\u5408\u308f\u305b\u304c\u6c42\u3081\u308b\u89e3\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4eca\u56de\u306fSAT\u3092MIS\u554f\u984c\u3092\u7d4c\u7531\u3057\u3066QUBO\u306e\u5f62\u3067\u5b9a\u5f0f\u5316\u3059\u308b\u3053\u3068\u3092\u76ee\u6a19\u3068\u3057\u3001\u7c21\u5358\u306a\u4f8b\u306e\u5834\u5408\u306b\u304a\u3044\u3066SAT\u304cMIS\u554f\u984c\u3078\u9084\u5143\u53ef\u80fd\u306a\u3053\u3068\u3092\u8aac\u660e\u3057\u305f\u3002SAT\u306b\u95a2\u3057\u3066\u306f\u4ed6\u306b\u3082\u88dc\u52a9\u5909\u6570\u3092\u7528\u3044\u3066AND,OR,NOT\u3092\u5b9f\u88c5\u3057\u3066\u89e3\u304f\u89e3\u6cd5\u306a\u3069\u3082\u8003\u3048\u3089\u308c\u308b\u306e\u3067\u305d\u3061\u3089\u3082\u5404\u81ea\u53c2\u7167\u3059\u308b\u3068\u826f\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4eca\u5f8c\u884c\u3044\u305f\u3044\u3053\u3068<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ima.umn.edu\/materials\/2014-2015\/MM8.5-14.15\/24035\/Final_Report_Team7.pdf\" target=\"_blank\" rel=\"noopener\">QA\u3092\u7528\u3044\u305f\u753b\u50cf\u5727\u7e2e\u306e\u8ad6\u6587<\/a>\u3092\u8aad\u3080\u3053\u3068<\/li>\n\n\n\n<li>Quantum computing\u306e\u672c\u3092\u8aad\u3080<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<\/h3>\n\n\n\n<p>\u5c0f\u6797\u53cb\u660e\uff08\u7de8\u96c6\uff1a\u89b3\u5c71\u6b63\u9053\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001Karp\u306e21\u306eNP\u5b8c\u5168\u554f\u984c\u306e\u4e00\u3064\u3067\u3042\u308b \u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT; satisfiability problem)\u306b\u95a2\u3057\u3066\u3001\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c (MIS; maximum independent set)\u306b\u5e30 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[21,39,82,112],"class_list":["post-651","post","type-post","status-publish","format-standard","hentry","category-hands-on","tag-karp21np","tag-sat","tag-82","tag-112"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT)\u306eQUBO\u8868\u73fe -\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c\u306b\u5e30\u7740\u3055\u305b\u308b\u65b9\u6cd5- T-QARD Harbor<\/title>\n<meta name=\"description\" content=\"\u672c\u8a18\u4e8b\u3067\u306f\u3001Karp\u306e21\u306eNP\u5b8c\u5168\u554f\u984c\u306e\u4e00\u3064\u3067\u3042\u308b \u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT; satisfiability problem)\u306b\u95a2\u3057\u3066\u3001\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c (MIS; maximum independent set)\u306b\u5e30\u7740\u3057\u3066\u3001\u554f\u984c\u3092QUBO\u8868\u73fe\u306b\u5909\u63db\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3059\u308b\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/07\/03\/sat-\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c\u306e\u30a4\u30b8\u30f3\u30b0\u8868\u73fe-by-\u5c0f\u6797\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT)\u306eQUBO\u8868\u73fe -\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c\u306b\u5e30\u7740\u3055\u305b\u308b\u65b9\u6cd5- T-QARD Harbor\" \/>\n<meta property=\"og:description\" content=\"\u672c\u8a18\u4e8b\u3067\u306f\u3001Karp\u306e21\u306eNP\u5b8c\u5168\u554f\u984c\u306e\u4e00\u3064\u3067\u3042\u308b \u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT; satisfiability problem)\u306b\u95a2\u3057\u3066\u3001\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c (MIS; maximum independent set)\u306b\u5e30\u7740\u3057\u3066\u3001\u554f\u984c\u3092QUBO\u8868\u73fe\u306b\u5909\u63db\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3059\u308b\u3002\" \/>\n<meta property=\"og:url\" content=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/07\/03\/sat-\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c\u306e\u30a4\u30b8\u30f3\u30b0\u8868\u73fe-by-\u5c0f\u6797\/\" \/>\n<meta property=\"og:site_name\" content=\"T-QARD Harbor\" \/>\n<meta property=\"article:published_time\" content=\"2018-07-03T03:00:09+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/sat_graph1.png\" \/>\n<meta name=\"author\" content=\"T-QARD Crews\" 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