{"id":25679,"date":"2021-04-23T21:52:32","date_gmt":"2021-04-23T13:52:32","guid":{"rendered":"https:\/\/swarma.org\/?p=25679"},"modified":"2021-04-23T21:52:32","modified_gmt":"2021-04-23T13:52:32","slug":"physics-reports%e6%9c%80%e6%96%b0%e7%bb%bc%e8%bf%b0%ef%bc%9a%e8%a7%a3%e5%86%b3%e7%89%a9%e7%90%86%e3%80%81%e7%94%9f%e7%89%a9%e3%80%81%e7%bb%8f%e6%b5%8e%e4%b8%ad%e7%9a%84%e7%a8%b3%e5%ae%9a%e5%8c%b9","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=25679","title":{"rendered":"Physics Reports\u6700\u65b0\u7efc\u8ff0\uff1a\u89e3\u51b3\u7269\u7406\u3001\u751f\u7269\u3001\u7ecf\u6d4e\u4e2d\u7684\u7a33\u5b9a\u5339\u914d"},"content":{"rendered":"
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<\/strong>\u770b\u7740\u8fc5\u901f\u589e\u957f\u7684\u79bb\u5a5a\u7387\uff0c\u6708\u8001\u53c8\u5f00\u59cb\u62c5\u5fc3\u8d77\u81ea\u5df1\u7684\u996d\u7897\u4e86\u3002\u660e\u660e\u5f88\u6e05\u695a\u4e16\u95f4\u7537\u5973\u7684\u7406\u60f3\u53e6\u4e00\u534a\u662f\u8c01\uff0c\u65e0\u5948\u4e00\u5fd7\u613f\u91cd\u5408\u592a\u591a\uff0c\u53ea\u80fd\u8c03\u5242\u4e00\u4e0b\u4e86\u3002\u54b3\u54b3\uff0c\u73b0\u5728\u8865\u8865\u8bfe\u5e94\u8be5\u8fd8\u6765\u5f97\u53ca\u30023 \u6708 16 \u65e5\u745e\u58eb\u5f17\u91cc\u5821\u5927\u5b66\u5f20\u7ffc\u6210\u56e2\u961f\u53d1\u8868\u5728 Physics Reports <\/em>\u4e0a\u7684\u7efc\u8ff0\u6587\u7ae0\u4e0d\u4ec5\u5bf9\u7a33\u5b9a\u5a5a\u59fb\u95ee\u9898\u8fdb\u884c\u4e86\u6982\u8ff0\uff0c\u8fd8\u8ba8\u8bba\u4e86\u8be5\u95ee\u9898\u4e0e\u6570\u5b66\u3001\u751f\u7269\u5b66\u7b49\u5b66\u79d1\u7684\u5173\u8054\uff0c\u5c24\u5176\u662f SMP \u5728\u7269\u7406\u5b66\u4e2d\u7684\u7406\u8bba\u3001\u5e94\u7528\u4e0e\u6700\u65b0\u8fdb\u5c55\u3002<\/strong><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u9648\u660a<\/span> | \u4f5c\u8005<\/strong><\/span><\/strong><\/p>\n

\u9093\u4e00\u96ea<\/span> | \u7f16\u8f91<\/strong><\/span><\/p>\n<\/section>\n


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\u8bba\u6587\u6807\u9898\uff1a
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The Stable Marriage Problem: An interdisciplinary review from the physicist\u2018s perspective<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span>https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0370157321000843<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u7a33\u5b9a\u5a5a\u59fb\u95ee\u9898\u8d77\u6e90\u4e8e\u6570\u5b66\uff0c\u968f\u540e\u5728\u7ecf\u6d4e\u5b66\u5f97\u5230\u53d1\u5c55\uff0c\u4e14\u5728\u8bb8\u591a\u9886\u57df\u90fd\u8868\u73b0\u51fa\u4e86\u5f88\u597d\u7684\u542f\u53d1\u6027\u3002\u8be5\u95ee\u9898\u4e8e 1962 \u5e74\u5728 Gale \u548c Shapley \u7684\u5f00\u521b\u6027\u6587\u7ae0[1]\u4e2d\u9996\u6b21\u51fa\u73b0\uff0c\u5e76\u5f15\u8d77\u4e86\u8bb8\u591a\u79d1\u5b66\u9886\u57df<\/span>\uff08\u5982\u7269\u7406\u5b66\u3001\u7ecf\u6d4e\u5b66\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\uff09<\/span>\u7684\u5173\u6ce8\u30023 \u6708 16 \u65e5\uff0c\u745e\u58eb\u5f17\u91cc\u5821\u5927\u5b66\u5f20\u7ffc\u6210\u56e2\u961f\u53d1\u8868\u5728 Physics Reports<\/em> \u4e0a\u7684\u7efc\u8ff0\u6587\u7ae0\u5bf9\u7a33\u5b9a\u5a5a\u59fb\u95ee\u9898\u8fdb\u884c\u4e86\u5168\u9762\u6982\u8ff0\uff0c\u7740\u91cd\u5f3a\u8c03\u4e86\u5b83\u7684\u591a\u5b66\u79d1\u6027\uff0c\u5c24\u5176\u5173\u6ce8\u7269\u7406\u5b66\u9886\u57df\u9488\u5bf9\u8be5\u95ee\u9898\u7684\u6700\u65b0\u6210\u679c\u3002<\/span><\/section>\n
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1. SMP\u95ee\u9898\u4ecb\u7ecd<\/strong><\/strong><\/p>\n<\/section>\n

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\u7a33\u5b9a\u5a5a\u59fb\u95ee\u9898<\/span>\uff08Stable Marriage Problem\uff0cSMP\uff09<\/span>\u9762\u5411\u4e00\u4e2a\u7531\u4e24\u79cd\u4e0d\u540c\u96c6\u5408\u7ec4\u6210\u7684\u7cfb\u7edf\uff0c\u4e24\u79cd\u96c6\u5408\u95f4\u7684\u5143\u7d20\u9700\u8981\u4f9d\u7167\u5404\u81ea\u7684\u504f\u597d\u8fdb\u884c\u4e00\u4e00\u914d\u5bf9\u3002\u4e3a\u4e86\u4fbf\u4e8e\u7406\u89e3\uff0c\u901a\u5e38\u5047\u8bbe\u8fd9\u4e24\u4e2a\u96c6\u5408\u5404\u5305\u542b N \u4f4d\u5f85\u5339\u914d\u7684\u7537\u58eb\u4e0e\u5973\u58eb\uff0c\u6bcf\u4e2a\u4eba\u90fd\u6709\u5176\u5bf9\u5f02\u6027\u7684\u504f\u597d\u5217\u8868\u3002SMP \u7684\u6700\u7ec8\u76ee\u7684\u662f\u5b9e\u73b0\u4e24\u4e2a\u96c6\u5408\u7684\u7a33\u5b9a\u5339\u914d\uff0c\u5373\u4e0d\u5b58\u5728\u4efb\u4f55\u4e00\u5bf9\u7537\u5973\u613f\u610f\u4e3a\u5f7c\u6b64\u653e\u5f03\u5f53\u524d\u7684\u4f34\u4fa3\u3002<\/span><\/section>\n

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\u8868 1 SMP \u95ee\u9898\u793a\u4f8b<\/span><\/section>\n
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\u4ee5\u8868 1 \u4e2d N=3 \u7684 SMP \u95ee\u9898\u4e3a\u4f8b\uff0c\u6bcf\u4e2a\u4eba\u7684\u635f\u5931\u8ba1\u7b97\u89c4\u5219\u5982\u4e0b\uff1a\u5982\u679c<\/span>m<\/span>1<\/span><\/sub><\/span><\/span><\/math-formula>\u4e0e<\/span>w1<\/span><\/sub><\/span><\/span><\/math-formula>\u914d\u5bf9\u5219\u635f\u5931\u4e3a 1\uff08\u8868\u793a\u4e3a<\/span>x1, 1<\/span><\/sub><\/span>=1<\/span><\/math-formula>\uff09\uff0c\u56e0\u4e3a<\/span>w1<\/span><\/sub><\/span><\/span><\/math-formula>\u662f<\/span>m1<\/span><\/sub><\/span><\/span><\/math-formula>\u7684\u7b2c 1 \u9009\u62e9\uff1b\u800c<\/span>w1<\/span><\/sub><\/span><\/span><\/math-formula>\u4e0e<\/span>m1<\/span><\/sub><\/span><\/span><\/math-formula>\u914d\u5bf9\u7684\u635f\u5931\u5219\u4e3a 2\uff08\u8868\u793a\u4e3a<\/span>y1, 1<\/span><\/sub><\/span>=2<\/span><\/math-formula>\uff09\uff0c\u56e0\u4e3a<\/span>m1<\/span><\/sub><\/span><\/span><\/math-formula>\u662f<\/span>w1<\/span><\/sub><\/span><\/span><\/math-formula>\u7684\u7b2c 2 \u9009\u62e9\uff1b\u540c\u7406\u6709<\/span>x2, 3<\/span><\/sub><\/span>=2<\/span><\/math-formula>\u3001<\/span>y3, 2<\/span><\/sub><\/span>=2<\/span><\/math-formula>\u7b49\u7b49\u3002<\/span><\/section>\n

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\u4e00\u4e2a\u5b8c\u6574\u7684\u5339\u914d\u89e3 M \u53ef\u4ee5\u8868\u793a\u4e3a<\/span>M={(mi<\/span><\/sub><\/span>, wj<\/sub><\/span>); i,j=1,\u2026, N<\/em>}<\/span><\/math-formula>\uff0c\u56e0\u6b64\u9488\u5bf9\u89c4\u6a21\u4e3a N \u7684\u7cfb\u7edf\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230<\/span>N!<\/span><\/math-formula>\u79cd\u53ef\u80fd\u7684\u5339\u914d\u89e3\uff0cSMP \u95ee\u9898\u9700\u8981\u89e3\u51b3\u7684\u5c31\u662f\u5bfb\u627e\u5176\u4e2d\u7684\u7a33\u5b9a\u89e3<\/span>\uff08stable solution\uff09<\/span>\u3002\u5728\u7a33\u5b9a\u89e3\u4e0b\u4e0d\u5b58\u5728\u4efb\u610f\u4e00\u5bf9 <\/span>(mi<\/span><\/sub><\/span>, wj<\/span><\/sub><\/span><\/span><\/math-formula>) <\/span><\/math-formula>\u4f7f\u5f97<\/span>mi<\/sub><\/span><\/span><\/math-formula>\u4e0e<\/span>wj<\/sub><\/span><\/span><\/math-formula>\u90fd\u613f\u610f\u4e3a\u5f7c\u6b64\u653e\u5f03\u5f53\u524d\u7684\u4f34\u4fa3\u3002\u56fe 1 \u4e3a\u8868 1 \u4e2d\u63d0\u5230\u7684\u793a\u4f8b\u7684\u4e24\u4e2a\u89e3\uff0c\u6839\u636e\u4e0a\u8ff0\u4ecb\u7ecd\u6613\u77e5\u5de6\u4fa7\u4e3a\u7a33\u5b9a\u89e3\u3002<\/span><\/section>\n
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\u56fe 1 SMP \u95ee\u9898\u7684\u89e3\uff1a\u5de6\u4fa7\u4e3a\u7a33\u5b9a\u89e3\uff0c\u800c\u53f3\u4fa7\u4e3a\u4e0d\u7a33\u5b9a\u89e3\u3002<\/span><\/section>\n
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\u5f53 N \u5f88\u5927\u65f6\uff0c\u5bfb\u627e SMP \u7684\u7a33\u5b9a\u89e3\u5e76\u975e\u6613\u4e8b\u3002\u4e3a\u89e3\u51b3\u8be5\u95ee\u9898\uff0cGale \u548c Shapley \u4e8e 1962 \u5e74\u63d0\u51fa\u4e86\u7b2c\u4e00\u4e2a\u4e5f\u662f\u6700\u8457\u540d\u7684\u5bfb\u627e SMP \u7279\u5b9a\u7a33\u5b9a\u89e3\u7684\u65b9\u6cd5\uff1aGale-Shapley<\/span>\uff08GS\uff09<\/span>\u7b97\u6cd5[1]\u3002GS \u7b97\u6cd5\u6709\u4e24\u4e2a\u7248\u672c\uff0c\u5206\u522b\u4ee5\u7537\u58eb\u548c\u5973\u58eb\u4e3a\u5bfc\u5411\u3002\u4e24\u79cd\u7248\u672c\u7684\u673a\u5236\u662f\u76f8\u540c\u7684\u4e3a\u7b80\u5355\u8d77\u89c1\u8fd9\u91cc\u4ec5\u4ecb\u7ecd\u7537\u58eb\u4e3b\u5bfc\u7684\u7248\u672c\uff1a<\/span><\/p>\n

1. \u5f00\u59cb\u65f6\uff0c\u6240\u6709\u7537\u58eb\u548c\u5973\u58eb\u90fd\u662f\u5355\u8eab\u3002<\/span><\/p>\n

2. \u9009\u62e9\u4e00\u4f4d\u5355\u8eab\u7537\u58eb<\/span>m<\/span>i<\/sub><\/span><\/span><\/math-formula>\u6839\u636e\u5176\u504f\u597d\u5217\u8868\u5bf9\u5973\u58eb\u6c42\u5a5a\uff1a<\/span><\/p>\n

a. m<\/span>i<\/sub><\/span><\/span><\/math-formula>\u5411\u4ed6\u7684\u504f\u597d\u5217\u8868\u4e2d\u6ca1\u6709\u8ffd\u6c42\u8fc7\u7684\u6700\u949f\u7231\u7684\u5973\u58ebw<\/span>j<\/sub><\/span><\/span><\/math-formula><\/span><\/math-formula>\u6c42\u5a5a\u3002<\/span><\/section>\n
b. \u5982\u679cw<\/span>j<\/sub><\/span><\/math-formula><\/span>\u6b63\u5904\u5355\u8eab\uff0c\u5219\u4e8c\u4eba\u8ba2\u5a5a\u3002<\/span><\/section>\n
c. \u5982\u679cw<\/span>j<\/sub><\/span><\/math-formula><\/span>\u5df2\u7ecf\u4e0e\u53e6\u5916\u4e00\u4f4d\u7537\u58eb<\/span>mp<\/sub><\/span><\/span><\/math-formula>\u8ba2\u5a5a\u4e14<\/span>yj, p<\/sub><\/span><\/math-formula><yj, i<\/sub><\/span><\/math-formula><\/span><\/math-formula>\uff0c\u5219w<\/span>j<\/sub><\/span><\/math-formula><\/span>\u56de\u7edd<\/span>mi<\/sub><\/span><\/span><\/math-formula>\uff0c<\/span>m<\/span>i<\/sub><\/span><\/span><\/math-formula>\u4f9d\u7136\u4fdd\u6301\u5355\u8eab\u3002<\/span><\/section>\n
d. \u5982\u679cw<\/span>j<\/sub><\/span><\/math-formula><\/span>\u5df2\u7ecf\u4e0e\u53e6\u5916\u4e00\u4f4d\u7537\u58eb<\/span>mp<\/sub><\/span><\/span><\/math-formula>\u8ba2\u5a5a\u4e14<\/span>yj, p<\/sub><\/span><\/math-formula>>yj, i<\/sub><\/span><\/math-formula>\uff0c<\/span><\/math-formula>\u5219w<\/span>j<\/sub><\/span><\/math-formula><\/span>\u63a5\u53d7<\/span>m<\/span>i<\/sub><\/span><\/span><\/math-formula>\uff0c<\/span>mp<\/sub><\/span><\/span><\/math-formula>\u53d8\u4e3a\u5355\u8eab\u3002<\/span><\/span><\/span><\/span><\/section>\n
3. \u7b97\u6cd5\u4f1a\u91cd\u590d\u6b65\u9aa4 2 \u76f4\u81f3\u6240\u6709\u7537\u58eb\u90fd\u627e\u5230\u5176\u4f34\u4fa3\u3002<\/span><\/section>\n

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\u53ef\u4ee5\u8bc1\u660e\u8be5\u7b97\u6cd5\u53ef\u4ee5\u6536\u655b\u5230\u7a33\u5b9a\u89e3\uff0c\u4e14\u4f1a\u5f97\u5230\u5bf9\u7537\u58eb\u800c\u8a00\u6700\u597d\u7684\u89e3\u51b3\u65b9\u6cd5\uff0c\u5373\u5c3d\u53ef\u80fd\u5730\u4f18\u5148\u6ee1\u8db3\u7537\u58eb\u7684\u9700\u6c42<\/span>\uff08\u5177\u4f53\u8bc1\u660e\u53c2\u8003\u539f\u6587\u7b2c\u56db\u90e8\u5206\uff09<\/span>\u3002\u5973\u58eb\u4e3b\u5bfc\u7684\u7248\u672c\u4e0e\u4e0a\u8ff0\u7b97\u6cd5\u7b49\u4ef7\uff0c\u53ea\u662f\u8ffd\u6c42\u8005\u53d8\u4e3a\u4e86\u5973\u58eb\u3002<\/span><\/section>\n
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\u672c\u8282\u4ecb\u7ecd\u4e86\u6700\u7b80\u5355\u7248\u672c\u7684 SMP\uff0c\u9664\u6b64\u4e4b\u5916\u8be5\u7efc\u8ff0\u8fd8\u9488\u5bf9\u591a\u79cd SMP \u53d8\u4f53\u8fdb\u884c\u4e86\u4ecb\u7ecd\u3002\u5982\u4fe1\u606f\u5b8c\u5168\u60c5\u51b5\u4e0b\u7684\u5168\u5c40\u6700\u4f18\u89e3\u4e0e\u6700\u5c0f\u5316\u7537\u5973\u4e0d\u5e73\u7b49\u7684\u89e3\uff0c\u4ee5\u53ca\u7537\u5973\u4eba\u6570\u4e0d\u5e73\u7b49\u6216\u504f\u597d\u5217\u8868\u5173\u8054\u4e0d\u5b8c\u6574\u60c5\u51b5\u4e0b\u7684\u89e3\u3002<\/span><\/section>\n
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3. SMP\u4e0e\u7269\u7406\u5b66<\/strong><\/strong><\/p>\n<\/section>\n

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3.1 SMP \u7684\u7269\u7406\u89e3\u91ca<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n<\/h3>\n
\u5982\u524d\u6587\u6240\u8ff0\uff0cSMP \u7684\u7a33\u5b9a\u6761\u4ef6\u4e0e\u4f18\u5316\u8fc7\u7a0b\u90fd\u662f\u503c\u5f97\u7814\u7a76\u7684\uff0c\u7269\u7406\u5b66\u5bb6\u5bf9\u4e8e\u540e\u8005\u5c24\u5176\u719f\u6089\uff1a\u7269\u7406\u5b66\u4e2d\u4f1a\u9047\u5230\u8bb8\u591a\u4e0d\u540c\u7c7b\u578b\u7684\u4f18\u5316\u95ee\u9898<\/strong>\uff0c\u8fd9\u4e9b\u95ee\u9898\u9700\u8981\u4f18\u5316\u8ddd\u79bb\u3001\u901f\u5ea6\u3001\u4e8b\u4ef6\u7b49\u591a\u79cd\u7269\u7406\u91cf\u3002\u800c SMP \u53ef\u4ee5\u4f5c\u4e3a\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u6765\u7814\u7a76\u3002\u4f17\u6240\u5468\u77e5\uff0c\u5e73\u8861\u7edf\u8ba1\u529b\u5b66\u4e0e\u7ec4\u5408\u4f18\u5316\u6709\u7740\u5171\u540c\u7684\u6839\u6e90[2]\u3002\u4ee5\u5bf9\u76f8\u53d8\u7684\u7814\u7a76\u4e3a\u4f8b\uff0c\u5176\u7814\u7a76\u5bf9\u8c61\u4e0d\u9700\u8981\u5c40\u9650\u4e8e\u7269\u7406\u7cfb\u7edf\uff0c\u800c\u53ef\u4ee5\u6269\u5145\u4e3a\u591a\u79cd\u7ec4\u5408\u4f18\u5316\u95ee\u9898\uff0c\u5982\u968f\u673a\u7f51\u7edc\u4e0a\u7684\u6e17\u6d41\u73b0\u8c61\u3002\u56e0\u6b64\u7269\u7406\u5b66\u4e0e SMP \u4f18\u5316\u7684\u5173\u8054\u662f\u5341\u5206\u81ea\u7136\u7684\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6b63\u5982\u524d\u6587\u6240\u8bf4\uff0cSMP \u7684\u76ee\u7684\u662f\u5bfb\u627e\u4f7f\u6bcf\u4e2a\u4e2a\u4f53\u90fd\u90fd\u6ee1\u610f\u7684\u914d\u5bf9\u65b9\u6848\u3002\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6bcf\u4e2a\u4eba\u90fd\u5728\u8003\u8651\u81ea\u8eab\u800c\u975e\u6574\u4f53\u7684\u5229\u76ca\u3002\u8fd9\u6837\u7684\u7a33\u5b9a\u5f62\u5f0f\u79f0\u4e3a\u7eb3\u4ec0\u5747\u8861<\/strong>\uff0c\u539f\u6587\u5728\u7b2c\u516d\u90e8\u5206<\/span>\uff08SMP \u4e0e\u7ecf\u6d4e\u5b66\u7684\u5173\u7cfb\uff09<\/span>\u5bf9\u5176\u8fdb\u884c\u4e86\u8be6\u7ec6\u7684\u63cf\u8ff0\u3002\u800c\u5728\u7269\u7406\u5b66\u5bb6\u6765\u770b\uff0cSMP \u8fd8\u5b58\u5728\u53e6\u4e00\u79cd\u6709\u8da3\u7684\u7a33\u5b9a\u72b6\u6001\uff1a\u5168\u5c40\u6700\u4f18\u89e3<\/strong><\/span>\uff08global minimum solution \u6216 Ground State\uff09<\/span>\uff0c\u5373\uff0c\u4f7f\u6240\u6709\u4eba\u7684\u603b\u635f\u5931\u6700\u5c0f\u5316\u7684\u89e3\u3002\u603b\u635f\u5931\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u6bcf\u4e2a\u4e2a\u4f53\u635f\u5931\u4e4b\u548c\uff0c\u5373 <\/span>X<\/span><\/em>+Y<\/em><\/span><\/math-formula>\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u56f4\u7ed5\u4e24\u79cd\u4e0d\u540c\u7684\u4f18\u5316\u76ee\u6807\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u4e9b\u6709\u8da3\u7684\u95ee\u9898\uff1a\u4e24\u79cd\u4f18\u5316\u76ee\u6807\u6709\u591a\u4e48\u4e0d\u540c\uff1f\u5b83\u4eec\u9762\u5bf9\u5916\u90e8\u6270\u52a8\u7684\u7a33\u5b9a\u6027\u5982\u4f55\uff0c\u6216\u8005\u8bf4\uff0c\u771f\u5b9e\u7cfb\u7edf\u5982\u4f55\u8fbe\u5230\u7a33\u5b9a\u72b6\u6001\uff1f\u4f5c\u8005\u4ece\u8fd9\u4e9b\u95ee\u9898\u51fa\u53d1\uff0c\u5bf9\u4e24\u79cd\u4f18\u5316\u76ee\u6807\u8fdb\u884c\u4e86\u5b9a\u91cf\u4e0e\u5b9a\u6027\u5206\u6790\uff0c\u9610\u660e\u4e86\u5168\u5c40\u6700\u4f18\u89e3\u4f9d\u7136\u503e\u5411\u4e8e\u8ba9\u4e2a\u4f53\u505a\u51fa\u81ea\u79c1\u7684\u51b3\u5b9a\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4ece\u5b9a\u6027\u7684\u89d2\u5ea6\u6765\u8bb2\uff0c\u5168\u5c40\u6700\u4f18\u89e3\u8868\u793a\u7684\u6a21\u578b\u4e2d\u50cf\u662f\u5b58\u5728\u7740\u4e00\u4e2a\u5a92\u4eba\u4ece\u4e2d\u64ae\u5408\u7537\u5973\u53cc\u65b9\uff0c\u8fd9\u4f7f\u5f97\u7ed3\u679c\u5bf9\u6574\u4f53\u6700\u4f18\u3002\u800c\u7a33\u5b9a\u89e3\u8868\u793a\u7684\u6a21\u578b\u5219\u66f4\u50cf\u662f\u4e00\u4e2a\u4fe1\u606f\u5b8c\u5168\u516c\u5f00\u7684\u81ea\u7531\u5a5a\u604b\u5e02\u573a\uff0c\u6bcf\u4e2a\u4eba\u90fd\u7406\u6027\u5730\u5173\u6ce8\u81ea\u5df1\u7684\u5229\u76ca\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\n
3.2 \u7a33\u5b9a\u89e3\u7684\u6570\u91cf<\/span><\/strong><\/section>\n<\/h3>\n
 <\/span><\/section>\n
\u4e3a\u4e86\u8fdb\u884c\u5bf9\u4e24\u79cd\u4f18\u5316\u76ee\u6807\u7684\u5b9a\u91cf\u5206\u6790\uff0c\u4f5c\u8005\u5bf9 SMP \u8fdb\u884c\u4e86\u66f4\u52a0\u7b26\u53f7\u5316\u7684\u63cf\u8ff0\u3002\u9996\u5148\u9700\u8981\u8865\u5145\u201c\u963b\u585e\u5bf9<\/span>\uff08blocking pair\uff09<\/span>\u201d\u7684\u6982\u5ff5\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u5339\u914d\u7b56\u7565 M\uff0c\u5982\u679c m \u548c w \u5e76\u975e\u60c5\u4fa3\u800c\u4e8c\u4eba\u90fd\u5e0c\u671b\u6210\u4e3a\u5f7c\u6b64\u7684\u60c5\u4fa3\uff0c\u5219\u79f0(m,w)\u4e3a\u4e00\u4e2a\u963b\u585e\u5bf9<\/strong>\u3002\u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u91cd\u65b0\u5b9a\u4e49\u7a33\u5b9a\u89e3\uff1a\u4e00\u4e2a\u4e0d\u5b58\u5728\u963b\u585e\u5bf9\u7684\u5339\u914d\u7b56\u7565\u3002\u5176\u6b21\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 y(w,m)\u8868\u793a m \u5728 w \u7684\u504f\u597d\u5217\u8868\u4e2d\u7684\u6392\u540d\uff0c\u540c\u7406\u4e5f\u53ef\u4ee5\u4f7f\u7528 x(m,w)\u6765\u8868\u793a w \u5728 m \u7684\u504f\u597d\u5217\u8868\u4e2d\u7684\u6392\u540d\u3002\u8fd9\u79cd\u6392\u540d\u53ef\u4ee5\u4e0e\u7edf\u8ba1\u7269\u7406\u5b66\u4e2d\u80fd\u91cf<\/strong>\u7684\u6982\u5ff5\u76f8\u5bf9\u5e94\uff0c\u56e0\u6b64\u4e0b\u6587\u4e2d\uff0cx \u548c y \u5c06\u8868\u793a\u80fd\u91cf\u3002\u5728\u7edf\u8ba1\u529b\u5b66\u4e2d\uff0c\u7cfb\u7edf\u901a\u5e38\u4f1a\u5411\u80fd\u91cf\u6700\u5c0f\u5316\u7684\u65b9\u5411\u6f14\u5316\u3002\u4e0e\u4e4b\u4e0d\u540c\u7684\u662f\uff0cSMP \u6240\u9700\u8fbe\u5230\u7684\u7a33\u5b9a\u89e3\u4e0d\u662f\u80fd\u91cf\u6700\u5c0f\u7684\u89e3\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4e0a\u6587\u5df2\u7ecf\u4ecb\u7ecd\u4e86\u4e00\u79cd\u5bfb\u627e\u7a33\u5b9a\u89e3\u7684\u6709\u6548\u65b9\u6cd5\uff1aGS \u7b97\u6cd5\uff0c\u901a\u5e38\u6765\u8bf4\u5b83\u4e5f\u88ab\u79f0\u4e3a GS \u7406\u8bba[1\uff0c3\uff0c4]\u3002GS \u7406\u8bba\u901a\u8fc7\u8bc1\u660e\u81f3\u5c11\u5b58\u5728\u4e00\u4e2a\u7a33\u5b9a\u89e3\u56de\u7b54\u4e86\u4e00\u4e2a\u6709\u5173 SMP \u7684\u57fa\u672c\u95ee\u9898\uff1a\u7a33\u5b9a\u89e3\u662f\u5426\u5b58\u5728\uff1f<\/span><\/section>\n

<\/span><\/section>\n
\u6839\u636e Knuth \u7684\u7406\u8bba[5]\uff0c\u9488\u5bf9\u89c4\u6a21\u4e3a N \u7684 SMP \u95ee\u9898\uff0c\u5728<\/span>N!<\/span><\/em><\/math-formula>\u79cd\u5339\u914d\u7b56\u7565\u4e2d\u968f\u673a\u9009\u62e9\u4e00\u79cd\uff0c\u8be5\u7b56\u7565\u4e3a\u7a33\u5b9a\u89e3\u7684\u6982\u7387 P \u4e3a<\/span><\/section>\n

<\/span><\/section>\n

<\/p>\n


<\/span><\/section>\n
\u5176\u4e2d<\/span>xi<\/sub><\/span>=x(i,i)<\/span><\/math-formula>\u8868\u793a<\/span>mi<\/sub><\/span><\/span><\/math-formula>\u4e0e<\/span>wi<\/sub><\/span><\/span><\/math-formula>\u7ed3\u5a5a\u7684\u80fd\u91cf<\/span>\uff08\u4e3a\u65b9\u6807\u8868\u8ff0\uff0c\u5177\u6709\u76f8\u540c\u4e0b\u6807\u7684\u7537\u5973\u5373\u4e3a\u7279\u5b9a\u7b56\u7565 M \u7ed9\u51fa\u7684\u60c5\u4fa3\uff09<\/span>\u3002\u516c\u5f0f 1 \u4e2d\u7684\u79ef\u5206\u53ea\u80fd\u9488\u5bf9\u5f88\u5c0f\u7684 N \u8fdb\u884c\u8ba1\u7b97\uff0c\u4e3a\u6b64 Boris Pittel \u5728\u5176\u6587\u7ae0[6]\u4e2d\u5bf9 N \u8d8b\u4e8e\u65e0\u7a77\u65f6\u7684\u60c5\u51b5\u8fdb\u884c\u4e86\u4f30\u8ba1\uff1a<\/span><\/section>\n

<\/span><\/section>\n

<\/p>\n


<\/span><\/section>\n
<\/span><\/section>\n
\u5176\u4e2d<\/span>\u0393(<\/span><\/math-formula>N)<\/span><\/math-formula>\u4e3a\u7b2c\u4e8c\u7c7b\u6b27\u62c9\u79ef\u5206\uff0c<\/span>\u0393<\/span><\/span>(N+1)=N!<\/span><\/math-formula>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u968f\u540e Dzierzawa \u548c Omero[7]\u53d1\u73b0 Pittel \u7684\u4f30\u8ba1\u5728\u6570\u503c\u4e0a\u5b58\u5728\u5f88\u5927\u8bef\u5dee\uff0c\u4e3a\u6b64\u4ed6\u4eec\u91cd\u65b0\u63a8\u5bfc\u51fa\u65b0\u7684\u8fd1\u4f3c\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/section>\n

<\/span><\/section>\n

<\/p>\n


<\/span><\/section>\n
<\/span><\/section>\n
\u5176\u4e2d S \u4e3a\u89c4\u6a21\u4e3a N \u7684 SMP \u4e2d\u7a33\u5b9a\u89e3\u7684\u8fd1\u4f3c\u6570\u91cf\u3002\u4e0a\u8ff0\u4e24\u8fd1\u4f3c\u516c\u5f0f\u7684\u8be6\u7ec6\u63a8\u5bfc\u8fc7\u7a0b\u53c2\u770b\u539f\u6587\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe 3 \u7a33\u5b9a\u89e3\u7684\u5e73\u5747\u6570\u91cf \u6bcf\u4e2a\u6570\u636e\u70b9\u5747\u4e3a\u4e3a 200 \u6b21\u968f\u673a\u5b9e\u9a8c\u5e73\u5747\u5f97\u5230\u3002\u865a\u7ebf\u4e3a\u516c\u5f0f 3 \u7684\u7406\u8bba\u503c\uff0c\u5b9e\u7ebf\u4e3a Pittel \u65b9\u6cd5\u7684\u7406\u8bba\u503c\u3002[7]<\/span><\/p>\n


<\/span><\/section>\n

\n
3.3 \u7537\u6027\u4e0e\u5973\u6027\u7684 GS \u80fd\u91cf<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n<\/h3>\n
\u4e0a\u6587\u5bf9\u7537\u6027\u5bfc\u5411\u7684 GS \u7b97\u6cd5\u8fdb\u884c\u4e86\u63cf\u8ff0\u3002\u6709\u8da3\u7684\u662f\uff0c\u5c3d\u7ba1\u7537\u6027\u5728\u8be5\u8fc7\u7a0b\u4e2d\u591a\u6b21\u53d7\u632b\uff0c\u4e14\u6700\u7ec8\u53ea\u80fd\u5f97\u5230\u4e00\u6b21\u79ef\u6781\u7684\u56de\u5e94\uff0c\u5374\u80fd\u5f97\u5230\u6700\u4f18\u7684\u7a33\u5b9a\u89e3\u3002\u800c\u5973\u6027\u5219\u638c\u63e1\u7740\u62d2\u7edd\u7684\u6743\u529b\uff0c\u5374\u4f1a\u5f97\u5230\u6700\u7cdf\u7cd5\u7684\u7a33\u5b9a\u89e3\u3002\u901a\u8fc7\u8ba1\u7b97\u7537\u6027\u4e0e\u5973\u6027\u7684\u80fd\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u9a8c\u8bc1\u4e0a\u8ff0\u73b0\u8c61\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5982\u679c\u6211\u4eec\u4f7f\u7528 r \u6765\u8868\u793a\u7537\u6027\u4e3b\u5bfc\u7684 GS \u7b97\u6cd5\u4e2d\u7537\u6027\u7684\u5e73\u5747\u8bf7\u6c42\u6b21\u6570\uff0c\u5219\u6709<\/span><\/section>\n

<\/span><\/section>\n

<\/p>\n


<\/section>\n
\u4f7f\u7528 r \u5206\u522b\u8868\u793a\u7537\u6027\u4e0e\u5973\u6027\u7684\u603b\u80fd\u91cf X\u3001Y \u6709<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n

<\/p>\n


<\/section>\n
\u4e0a\u8ff0\u516c\u5f0f\u7684\u8be6\u7ec6\u63a8\u5bfc\u8fc7\u7a0b\u53c2\u89c1\u539f\u6587\uff0c\u56fe 4 \u4e3a\u4e0d\u540c\u89c4\u6a21 SMP \u95ee\u9898\u4e0b\u7537\u6027\u4e0e\u5973\u6027\u80fd\u91cf\u7684\u53ef\u89c6\u5316\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe4 GS \u80fd\u91cf \u7537\u58eb\u4e3b\u5bfc\u7684 GS \u7b97\u6cd5\u4e2d\u7537\u6027\u4e0e\u5973\u6027\u7684\u80fd\u91cf\uff0c\u5176\u4e2d Y \u8f74\u4e3a\u5bf9\u6570\u5750\u6807\u3002[7]<\/span><\/p>\n

\n

<\/section>\n
3.4 \u7a33\u5b9a\u89e3\u4e0e\u5168\u5c40\u6700\u4f18\u89e3\u7684\u6bd4\u8f83<\/span><\/strong><\/span><\/section>\n<\/h3>\n

<\/span><\/section>\n
\u9664\u4e0a\u8ff0\u5bf9\u7a33\u5b9a\u89e3\u7684\u5206\u6790\u5916\uff0c\u6587\u7ae0\u8fd8\u4f7f\u7528\u7edf\u8ba1\u7269\u7406\u65b9\u6cd5\u4ecb\u7ecd\u4e86\u5168\u5c40\u6700\u4f18\u89e3\u5bf9\u5e94\u7684\u80fd\u91cf\u7684\u6c42\u89e3\u65b9\u6cd5\uff0c\u56fe 5 \u4e3a\u5168\u5c40\u6700\u4f18\u89e3 GS \u80fd\u91cf\u4e0e\u7cfb\u7edf\u89c4\u6a21\u7684\u5173\u7cfb\uff0c\u53d7\u7bc7\u5e45\u9650\u5236\u8fd9\u91cc\u4e0d\u505a\u5c55\u5f00\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
\u56fe 5 SMP \u57fa\u6001\u80fd\u91cf \u6a2a\u5750\u6807 n=N\/2<\/span><\/section>\n
 <\/span><\/section>\n
\u7814\u7a76\u7a33\u5b9a\u89e3\u4e0e\u5168\u5c40\u6700\u4f18\u89e3\u7684\u5173\u7cfb\u662f\u5341\u5206\u6709\u5fc5\u8981\u7684\uff0c\u8fd9\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u4e2a\u4f53\u7684\u81ea\u79c1\u884c\u4e3a\u4e0e\u793e\u4f1a\u6700\u4f73\u72b6\u6001\u7684\u5173\u7cfb\u3002\u6587\u7ae0\u8bc1\u660e\u4e86\u7a33\u5b9a\u89e3\u4e0e\u5168\u5c40\u6700\u4f18\u89e3\u4e4b\u95f4\u5b58\u5728\u7740\u4e00\u4e2a\u80fd\u9699\u3002\u4e0e SMP \u57fa\u6001\u80fd\u91cf\u76f8\u6bd4\uff0c\u7a33\u5b9a\u89e3\u5b58\u5728\u7740 19%\u7684\u6539\u8fdb\u7a7a\u95f4\u3002\u5728[9]\u4e2d\uff0cLage Castellanos \u548c Mulet \u4ecb\u7ecd\u4e86\u4ee5\u4e0b\u6307\u6807\uff1a<\/span><\/section>\n

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<\/span><\/section>\n
\u8be5\u6307\u6807\u8861\u91cf\u4e86 a \u4e0e b \u4e24\u79cd\u72b6\u6001\u95f4\u4e0d\u540c\u60c5\u4fa3\u7ec4\u5408\u7684\u6570\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5176\u89c6\u4f5c\u4e24\u79cd\u72b6\u6001\u95f4\u7684\u8ddd\u79bb\u3002\u5982\u56fe 6 \u6240\u793a\uff0c\u4e24\u79cd\u72b6\u6001\u95f4\u7684\u8ddd\u79bb\u4e3a 0.53\u3002\u8fd9\u610f\u5473\u7740\u4e24\u79cd\u72b6\u6001\u4e2d\u7ea6\u6709 50%\u7684\u60c5\u4fa3\u7ec4\u5408\u662f\u4e0d\u540c\u7684\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
\u56fe 6 \u5168\u5c40\u6700\u4f18\u72b6\u6001\u4e0e\u7a33\u5b9a\u72b6\u6001\u95f4\u7684\u8ddd\u79bb<\/span><\/section>\n
 <\/span><\/section>\n

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4. SMP\u4e0e\u5176\u4ed6\u5b66\u79d1<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


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4.1 SMP \u4e0e\u751f\u7269\u5b66<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n<\/h3>\n
\u5fae\u751f\u7269\u7fa4\u843d\u662f\u6307\u53ef\u4ee5\u5b58\u5728\u4e8e\u4e0d\u540c\u7c7b\u578b\u73af\u5883<\/span>\uff08\u5982\u571f\u58e4\u3001\u6d77\u6d0b\u751a\u81f3\u4eba\u4f53\uff09<\/span>\u4e2d\u7684\u5fae\u751f\u7269\u7fa4\u4f53\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u7fa4\u843d\u6d89\u53ca\u4e0d\u540c\u7c7b\u578b\u7684\u5fae\u751f\u7269\uff0c\u5e76\u4e14\u53ef\u80fd\u975e\u5e38\u590d\u6742<\/span>\uff08\u6570\u5343\u79cd\u4e0d\u540c\u7684\u7269\u79cd\u53ef\u4ee5\u5728\u5f88\u5c0f\u7684\u4f53\u79ef\u5185\u5171\u5b58\uff09<\/span>\uff0c\u4f46\u79d1\u5b66\u5bb6\u5df2\u7ecf\u8bc1\u660e\uff0c\u5b83\u4eec\u901a\u5e38\u662f\u4ee5\u591a\u79cd\u7a33\u5b9a\u72b6\u6001\u5b58\u5728\uff0c\u4e0d\u540c\u7a33\u5b9a\u72b6\u6001\u6709\u7740\u4e0d\u540c\u7684\u5171\u5b58\u7269\u79cd\u6bd4\u4f8b[11]\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u901a\u5e38\u6765\u8bf4\uff0c\u6bcf\u79cd\u5fae\u751f\u7269\u90fd\u6709\u5176\u7279\u5b9a\u7684\u8425\u517b\u7d20\u504f\u597d\u5217\u8868\uff0c\u5f53\u4e00\u4e2a\u5fae\u751f\u7269\u7fa4\u843d\u66b4\u9732\u5728\u8425\u517b\u7d20\u73af\u5883\u4e2d\u65f6\u3002\u4ed6\u4eec\u4fbf\u4f1a\u4f9d\u7167\u5217\u8868\u4f9d\u6b21\u6444\u53d6\u8425\u517b\u3002\u4f7f\u7528 SMP \u6765\u63cf\u8ff0\u5fae\u751f\u7269\u7fa4\u843d\u6f14\u5316\u53ef\u4ee5\u4f18\u96c5\u5730\u8bc1\u660e\u591a\u79cd\u7a33\u5b9a\u72b6\u6001\u7684\u5b58\u5728\uff0c\u4ee5\u53ca\u8fd9\u4e9b\u72b6\u6001\u4e4b\u95f4\u7684\u8f6c\u6362\u53ca\u6062\u590d\u80fd\u529b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5a5a\u59fb\u5173\u7cfb\u8868\u73b0\u4e3a\u5fae\u751f\u7269\u79cd\u7c7b\u548c\u8425\u517b\u7d20\u4e4b\u95f4\u7684\u4e00\u4e00\u5339\u914d\u3002\u5728\u66f4\u4e00\u822c\u7684\u6a21\u578b\u4e2d\uff0c\u6240\u6709\u7684\u5fae\u751f\u7269\u90fd\u53ef\u4ee5\u5229\u7528\u6240\u6709\u7684\u8425\u517b\u7d20\u3002\u5728\u5b9e\u9645\u60c5\u51b5\u4e2d\uff0c\u5fae\u751f\u7269\u53ea\u80fd\u6444\u53d6\u90e8\u5206\u8425\u517b\u7d20\uff0c\u8fd9\u4e00\u60c5\u51b5\u53ef\u4ee5\u901a\u8fc7\u504f\u597d\u5217\u8868\u4e0d\u5b8c\u6574\u7684 SMP \u53d8\u4f53\u6765\u8fdb\u884c\u5206\u6790\u3002<\/span><\/section>\n

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<\/section>\n

\u56fe7 \u5fae\u751f\u7269\u7fa4\u843d\u7684\u52a8\u6001\u6f14\u5316 \u9876\u90e8\u65b9\u6846\u663e\u793a\u4e86\u5fae\u751f\u7269\u548c\u8425\u517b\u7d20\u7684\u504f\u597d\u5217\u8868\u3002\uff08A\uff09\u5c55\u793a\u4e86\u5411\u539f\u672c\u5904\u4e8e\u6700\u4f73\u72b6\u6001\u7684\u7cfb\u7edf\u4e2d\u52a0\u5165\u5fae\u751f\u7269 M3 \u540e\u7cfb\u7edf\u7684\u6f14\u5316\u8fc7\u7a0b\uff1b\uff08B\uff09\u5c55\u793a\u4e86\u5411\u751f\u6001\u7cfb\u7edf\u4e2d\u52a0\u5165\u8425\u517b\u7d20 N3 \u540e\u7cfb\u7edf\u6062\u590d\u6700\u4f73\u72b6\u6001\u7684\u8fc7\u7a0b\u3002[12]<\/span><\/p>\n


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4.2 SMP \u4e0e\u7ecf\u6d4e\u5b66<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n<\/h3>\n
\u7ecf\u6d4e\u9886\u57df\u662f SMP \u6700\u6210\u529f\u7684\u9886\u57df\u4e4b\u4e00\u3002\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u8bb8\u591a\u5e02\u573a\u90fd\u975e\u5e38\u9002\u5408\u4f7f\u7528\u7a33\u5b9a\u5339\u914d\u7406\u8bba\u8fdb\u884c\u5efa\u6a21\u30022012 \u5e74 Shapley \u548c Roth \u5c31\u56e0\u5176\u5bf9\u7a33\u5b9a\u5339\u914d\u7406\u8bba\u7684\u7406\u8bba\u4e0e\u5b9e\u9a8c\u8d21\u732e\u800c\u88ab\u6388\u4e88\u4e86\u8bfa\u8d1d\u5c14\u7ecf\u6d4e\u5b66\u5956\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u533b\u751f\u5206\u914d\u5230\u533b\u9662\u7684\u95ee\u9898\u662f\u662f SMP \u7684\u4e3b\u8981\u5e94\u7528\u4e4b\u4e00\uff0c\u5b83\u662f\u901a\u8fc7\u5339\u914d\u7406\u8bba\u7814\u7a76\u7684\u7b2c\u4e00\u4e2a\u95ee\u9898\uff0c\u5e76\u542f\u53d1\u4e86\u968f\u540e\u7684\u5927\u90e8\u5206\u5de5\u4f5c\u300220 \u4e16\u7eaa 40 \u5e74\u4ee3\uff0c\u7a00\u7f3a\u7684\u533b\u5b66\u751f\u8d44\u6e90\u8feb\u4f7f\u7f8e\u56fd\u7684\u533b\u9662\u4e3a\u4f4e\u5e74\u7ea7\u7684\u5b66\u751f\u63d0\u4f9b\u5b9e\u4e60\u673a\u4f1a\uff0c\u8fd9\u65f6\u7684\u90e8\u5206\u5b66\u751f\u751a\u81f3\u8fd8\u6ca1\u6709\u786e\u5b9a\u81ea\u5df1\u7684\u7814\u7a76\u9886\u57df\u3002\u7531\u4e8e\u5e02\u573a\u7684\u706b\u7206\uff0c\u5982\u679c\u533b\u9662\u7684\u5b9e\u4e60\u9080\u8bf7\u88ab\u62d2\u7edd\uff0c\u5219\u5f88\u53ef\u80fd\u4f1a\u9519\u5931\u5411\u5176\u4ed6\u5b66\u751f\u63d0\u51fa\u9080\u7ea6\u7684\u673a\u4f1a\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n
\u56fe8 \u533b\u751f\u5206\u914d\u5230\u533b\u9662\u95ee\u9898<\/span><\/section>\n

<\/span><\/section>\n
\u901a\u8fc7\u4e0a\u8ff0\u65b9\u5f0f\u6784\u9020\u7684\u5e02\u573a\u663e\u7136\u4f1a\u5b58\u5728\u4e0d\u7a33\u5b9a\u7684\u5339\u914d\uff0c\u56e0\u4e3a\u6ca1\u6709\u8db3\u591f\u7684\u65f6\u95f4\u6765\u63d0\u51fa\u5bf9\u53cc\u65b9\u90fd\u6709\u5229\u7684\u62a5\u4ef7\u3002\u4e3a\u89e3\u51b3\u8be5\u95ee\u9898\uff0c\u533b\u9662\u89c4\u5b9a\u4e86\u62a5\u4ef7\u7684\u56de\u5e94\u671f\u9650\uff0c\u8feb\u4f7f\u5b66\u751f\u8f83\u65e9\u5730\u505a\u51fa\u51b3\u5b9a\uff0c\u800c\u6ca1\u6709\u65f6\u95f4\u77e5\u9053\u4ed6\u4eec\u662f\u5426\u4f1a\u6536\u5230\u66f4\u597d\u7684\u62a5\u4ef7\u3002\u4e3a\u89e3\u51b3\u8be5\u95ee\u9898\uff0c\u7f8e\u56fd\u5728\u4e0a\u4e16\u7eaa\u4e2d\u53f6\u63d0\u51fa\u4e86\u56fd\u5bb6\u5c45\u6c11\u5339\u914d\u8ba1\u5212<\/span>\uff08NRMP\uff09<\/span>\uff0cRoth \u7684\u5de5\u4f5c[10]\u8bc1\u660e\u4e86 NRMP \u7b97\u6cd5\u4e0e\u6807\u51c6 GS \u7b97\u6cd5\u76f8\u540c\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u9664\u4e0a\u8ff0\u5b66\u79d1\u5916\uff0c\u539f\u6587\u8fd8\u8ba8\u8bba\u4e86 SMP \u5728\u6570\u5b66\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u76f8\u5173\u7814\u7a76\uff0c\u5e76\u5c55\u793a\u4e86\u7406\u8bba\u7ed3\u679c\u3001\u5e94\u7528\uff0c\u4ee5\u53ca\u53d7\u5176\u542f\u53d1\u7684\u591a\u79cd\u6a21\u578b\u3002<\/span><\/section>\n
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5. \u603b\u7ed3<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

SMP \u672c\u8eab\u5e76\u4e0d\u590d\u6742\uff0c\u4f46\u5b83\u5374\u5f15\u8d77\u4e86\u4eba\u4eec\u7684\u6781\u5927\u5174\u8da3\uff0c\u5e76\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u573a\u666f\u3002SMP \u662f\u5bf9\u73b0\u5b9e\u7684\u7406\u60f3\u4f46\u5408\u7406\u7684\u8868\u8ff0\uff0c\u5b83\u6293\u4f4f\u4e86\u8bb8\u591a\u4e8c\u5206\u7cfb\u7edf\u7684\u672c\u8d28\u3002\u7531 SMP \u539f\u7406\u51fa\u53d1\uff0c\u53ef\u4ee5\u5f97\u5230\u8bb8\u591a\u540c\u6837\u7b80\u5355\u4f46\u4e0d\u5e73\u51e1\u7684\u6a21\u578b\u3002\u4ee5\u5750\u5ea7\u4f4d\u95ee\u9898<\/strong><\/span>\uff08Seating Problem\uff09<\/span>\u4e3a\u4f8b\uff0c\u5c06 N \u4e2a\u4eba<\/span>\uff08\u4e0d\u533a\u5206\u7537\u5973\uff09<\/span>\u5b89\u6392\u5728\u4e00\u4e2a\u6709\u7740 N \u4e2a\u5ea7\u4f4d\u7684\u5706\u684c\u4e0a\uff0c\u6bcf\u4e2a\u4eba\u90fd\u6709\u4e00\u4e2a\u5bf9\u76f8\u90bb\u5ea7\u4f4d\u4e0a\u7684\u4eba\u7684\u504f\u597d\u5217\u8868\u3002\u7531\u6b64\u53ef\u4ee5\u5f97\u5230\u591a\u79cd\u5b89\u6392\u5ea7\u4f4d\u7684\u65b9\u5f0f\uff0c\u95ee\u9898\u7684\u76ee\u6807\u662f\u627e\u5230\u5176\u4e2d\u7684\u6700\u4f18\u89e3\u4f7f\u5f97\u4efb\u4f55\u4eba\u90fd\u4e0d\u5e0c\u671b\u66f4\u6362\u81ea\u5df1\u7684\u5ea7\u4f4d\u3002<\/span><\/section>\n
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\u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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[1] Gale, D., and L. S. Shapley. \u201cCollege Admissions and the Stability of Marriage.\u201d The American Mathematical Monthly, vol. 69, no. 1, 1962, pp. 9\u201315. JSTOR, www.jstor.org\/stable\/2312726. Accessed 14 Apr. 2021.<\/span><\/p>\n

[2] Kumar P R, Wainwright M J, Zecchina R. Mathematical Foundations of Complex Networked Information Systems: Politecnico Di Torino, Verr\u00e8s, Italy 2009[M]. Springer, 2015.<\/span><\/p>\n

[3] Gusfield D. Three fast algorithms for four problems in stable marriage[J]. SIAM Journal on Computing, 1987, 16(1): 111-128.<\/span><\/p>\n

[4] Dubins, L. E., and D. A. Freedman. \u201cMachiavelli and the Gale-Shapley Algorithm.\u201d The American Mathematical Monthly, vol. 88, no. 7, 1981, pp. 485\u2013494. JSTOR, www.jstor.org\/stable\/2321753. Accessed 20 Apr. 2021.<\/span><\/p>\n

[5] Donald E K. The art of computer programming[J]. Sorting and searching, 1999, 3: 426-458.<\/span><\/p>\n

[6] Pittel B. The average number of stable matchings[J]. SIAM Journal on Discrete Mathematics, 1989, 2(4): 530-549.<\/span><\/p>\n

[7] Dzierzawa M, Om\u00e9ro M J. Statistics of stable marriages[J]. Physica A: Statistical Mechanics and its Applications, 2000, 287(1-2): 321-333.<\/span><\/p>\n

[8] Omero M, Dzierzawa M, Marsili M, et al. Scaling behavior in the stable marriage problem[J]. Journal de Physique I, 1997, 7(12): 1723-1732.<\/span><\/p>\n

[9] Lage-Castellanos A, Mulet R. The marriage problem: From the bar of appointments to the agency[J]. Physica A: Statistical Mechanics and its Applications, 2006, 364: 389-402.<\/span><\/p>\n

[10] Roth A E. The evolution of the labor market for medical interns and residents: a case study in game theory[J]. Journal of political Economy, 1984, 92(6): 991-1016.<\/span><\/p>\n

[11] Franzosa E A, Hsu T, Sirota-Madi A, et al. Sequencing and beyond: integrating molecular’omics’ for microbial community profiling[J]. Nature Reviews Microbiology, 2015, 13(6): 360-372.<\/span><\/p>\n

[12] Goyal A, Dubinkina V, Maslov S. Multiple stable states in microbial communities explained by the stable marriage problem[J]. The ISME journal, 2018, 12(12): 2823-2834.<\/span><\/p>\n


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\uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n


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\u590d\u6742\u79d1\u5b66\u6700\u65b0\u8bba\u6587<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science<\/span>\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/span>
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\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong>
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