{"id":50444,"date":"2022-11-25T09:52:41","date_gmt":"2023-08-27T21:30:27","guid":{"rendered":"https:\/\/www.silicloud.com\/zh\/blog\/%e6%9c%80%e8%bf%91%e7%bb%8f%e5%b8%b8%e5%90%ac%e5%88%b0%e7%9a%84quorum%e6%98%af%e4%b8%80%e4%b8%aa%e6%af%94%e7%ae%80%e5%8d%95%e5%a4%9a%e6%95%b0%e6%8a%95%e7%a5%a8%e6%9b%b4%e5%b8%b8%e8%a7%81%e5%92%8c\/"},"modified":"2024-04-29T02:24:57","modified_gmt":"2024-04-28T18:24:57","slug":"%e6%9c%80%e8%bf%91%e7%bb%8f%e5%b8%b8%e5%90%ac%e5%88%b0%e7%9a%84quorum%e6%98%af%e4%b8%80%e4%b8%aa%e6%af%94%e7%ae%80%e5%8d%95%e5%a4%9a%e6%95%b0%e6%8a%95%e7%a5%a8%e6%9b%b4%e5%b8%b8%e8%a7%81%e5%92%8c","status":"publish","type":"post","link":"https:\/\/www.silicloud.com\/zh\/blog\/%e6%9c%80%e8%bf%91%e7%bb%8f%e5%b8%b8%e5%90%ac%e5%88%b0%e7%9a%84quorum%e6%98%af%e4%b8%80%e4%b8%aa%e6%af%94%e7%ae%80%e5%8d%95%e5%a4%9a%e6%95%b0%e6%8a%95%e7%a5%a8%e6%9b%b4%e5%b8%b8%e8%a7%81%e5%92%8c\/","title":{"rendered":"\u6700\u8fd1\u7ecf\u5e38\u542c\u5230\u7684Quorum\u662f\u4e00\u4e2a\u6bd4\u7b80\u5355\u591a\u6570\u6295\u7968\u66f4\u5e38\u89c1\u548c\u5f3a\u5927\u7684\u6982\u5ff5"},"content":{"rendered":"<p>\u6700\u8fd1\uff0c&#8221;Quorum&#8221;\u8fd9\u4e2a\u8bcd\u53d8\u5f97\u5e76\u4e0d\u7f55\u89c1\u4e86\u3002\u5728\u7c7b\u4f3cZookeeper\u3001etcd\u3001Serf\u8fd9\u6837\u7684\u96c6\u7fa4\u73af\u5883\u4e2d\uff0c\u4ee5\u53ca\u7c7b\u4f3cCassandra\u3001Riak\u8fd9\u6837\u7684\u5206\u5e03\u5f0f\u6570\u636e\u5e93\uff08NoSQL\u7c7b\u578b\uff09\u4e2d\uff0c\u6211\u4eec\u7ecf\u5e38\u542c\u5230\u8fd9\u4e2a\u8bcd\uff0c\u5b83\u6307\u7684\u662f\u786e\u4fdd\u6570\u636e\u590d\u5236\u7684\u4e00\u81f4\u6027\u673a\u5236\u3002<\/p>\n<p>\u7136\u800c\uff0c\u5373\u4f7f\u8bfb\u4e86\u8bb8\u591a\u5e7b\u706f\u7247\u548c\u7f51\u4e0a\u6587\u7ae0\uff0c\u6211\u8fd8\u662f\u89c9\u5f97&#8221;Quorum&#8221;\u8fd9\u4e2a\u8bcd\u7684\u610f\u601d\u57fa\u672c\u4e0a\u662f\u6307\u7531\u591a\u6570\u8282\u70b9\u8fdb\u884c\u591a\u6570\u51b3\u7b56\u3002<\/p>\n<p>\u5c3d\u7ba1\u5982\u6b64\uff0c\u4e3a\u4ec0\u4e48\u88ab\u79f0\u4e3a\u201cQuorum\u201d\uff1f\u7531\u4e8e\u5bf9\u8fd9\u4e2a\u95ee\u9898\u611f\u5230\u597d\u5947\uff0c\u6240\u4ee5\u6211\u501f\u6b64\u673a\u4f1a\u8fdb\u884c\u4e86\u8c03\u67e5\u3002<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u60f3\u5c06&#8221;Quorum&#8221;\u5b9a\u4e49\u4e3a\u4e00\u4e2a\u975e\u5e38\u62bd\u8c61\u4e14\u5f3a\u5927\u7684\u6982\u5ff5\uff0c\u5b83\u662f\u5c06\u591a\u6570\u51b3\u5b9a\u7684\u6982\u5ff5\u63a8\u5e7f\u7684\u7ed3\u679c\u3002<\/p>\n<h1>\u5728\u5206\u6563\u7cfb\u7edf\u4e2d\uff0c\u6570\u636e\u7684\u590d\u5236<\/h1>\n<p>\u6700\u8fd1\uff0c\u5206\u6563\u7cfb\u7edf\u53d8\u5f97\u8d8a\u6765\u8d8a\u5e38\u89c1\u3002\u5728\u5206\u6563\u7cfb\u7edf\u4e2d\uff0c\u6570\u636e\u51e0\u4e4e\u4e0d\u4f1a\u88ab\u4fdd\u5b58\u5728\u4e00\u4e2a\u5730\u65b9\uff0c\u800c\u662f\u4f1a\u88ab\u590d\u5236\u5e76\u4fdd\u5b58\u5728\u591a\u4e2a\u8282\u70b9\u4e0a\uff0c\u5373\u5b58\u5728\u591a\u4e2a\u526f\u672c\u3002<\/p>\n<p>\u901a\u8fc7\u590d\u5236\u53ef\u4ee5\u63d0\u9ad8\u8bfb\u53d6\u541e\u5410\u91cf\uff0c\u901a\u8fc7\u5c06\u590d\u5236\u8fd4\u56de\u7ed9\u5ba2\u6237\u7aef\u53ef\u4ee5\u63d0\u9ad8\u8bfb\u53d6\u901f\u5ea6\uff0c\u4f46\u4ece\u5206\u5e03\u5f0f\u7cfb\u7edf\u7684&#8221;\u6545\u969c\u5bb9\u5fcd\u6027&#8221;\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u5373\u4f7f\u5176\u4ed6\u8282\u70b9\u505c\u6b62\uff0c\u4e5f\u53ef\u4ee5\u8fdb\u884c\u6570\u636e\u7684\u8bfb\u53d6\u548c\u5199\u5165\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6570\u636e\u7684\u53ef\u7528\u6027\u589e\u5f3a\u4e86\u3002<\/p>\n<p>\u7136\u800c\uff0c\u8fd9\u5e76\u4e0d\u662f\u514d\u8d39\u7684\uff0c\u968f\u7740\u590d\u5236\u7684\u589e\u52a0\uff0c\u4e00\u65e6\u5728\u6570\u636e\u4fee\u6539\u65f6\u65e0\u6cd5\u6709\u6548\u5730\u7ba1\u7406\u590d\u5236\u54c1\uff0c\u95ee\u9898\u5c31\u4f1a\u53d8\u5f97\u66f4\u52a0\u590d\u6742\u3002\u5982\u679c\u590d\u5236\u54c1\u7684\u5185\u5bb9\u51fa\u73b0\u5dee\u5f02\uff0c\u90a3\u4e48\u5c31\u5f88\u96be\u4e3a\u5ba2\u6237\u63d0\u4f9b\u4e00\u81f4\u7684\u8bfb\u53d6\u6570\u636e\u3002<\/p>\n<p>\u5728\u5206\u6563\u7cfb\u7edf\u4e2d\uff0c\u7531\u4e8e\u591a\u4e2a\u8fdb\u7a0b\u7ec4\u88ab\u7f51\u7edc\u9694\u79bb\uff0c\u56e0\u6b64\u6211\u4eec\u5e0c\u671b\u5b83\u4eec\u80fd\u5728\u7f51\u7edc\u88ab\u5206\u5272\u7684\u60c5\u51b5\u4e0b\u4ecd\u80fd\u6b63\u5e38\u5de5\u4f5c\uff08\u5373\u5177\u6709\u7f51\u7edc\u5206\u533a\u5bb9\u5fcd\u6027\uff09\u3002<\/p>\n<p>2000\u5e74\u4ee3\u521d\u671f\u306b\u8a3c\u660e\u3055\u308c\u305f\u6709\u540d\u306aCAP\u5b9a\u7406\u306b\u3088\u308c\u3070\u3001\u8fd9\u4e2aC\u3001A\u3001P\u4e09\u4e2a\u5c5e\u6027\u65e0\u8bba\u5982\u4f55\u90fd\u4e0d\u80fd\u540c\u65f6\u6ee1\u8db3\uff0c\u53ea\u80fd\u540c\u65f6\u6ee1\u8db3\u5176\u4e2d\u4e24\u4e2a\u3002<\/p>\n<h1>\u7ecf\u5e38\u542c\u5230\u7684Quorum\u662f\u6307\u591a\u6570\u51b3\u5b9a\/\u8fc7\u534a\u6570\u5bf9\u5417\uff1f<\/h1>\n<p>\u6211\u6709\u70b9\u504f\u79bb\u4e86\u8bdd\u9898\uff0c\u4f46\u5728\u590d\u5236\u7ba1\u7406\u65b9\u6cd5\u4e2d\uff0c\u7ecf\u5e38\u542c\u8bf4\u7684\u662f\u4f7f\u7528Quorum\u7684\u65b9\u6cd5\u3002\uff08\u8fd8\u6709\u5176\u4ed6\u65b9\u6cd5\uff0c\u5982ROWA\uff08Read One Write All\uff09\uff0cPrimary Copy ROWA\uff09<\/p>\n<p>\u8fd9\u4e9b\u88ab\u79f0\u4e3aNoSQL\uff08\u5982Cassandra\u3001Riak\u7b49\uff09\u4ee5\u53caPaxos\u3001RAFT\u7b49\u7b97\u6cd5\uff0c\u662f\u5728\u8457\u540d\u7684\u5206\u5e03\u5f0f\u4e00\u81f4\u7b97\u6cd5\u548c\u9886\u5bfc\u8005\u9009\u4e3e\u7b97\u6cd5\u4e2d\u4f7f\u7528\u7684\u3002<\/p>\n<p>\u5728\u4e2d\u56fd\uff0c\u8fd9\u4e2aQuorum\u7ecf\u5e38\u88ab\u89e3\u91ca\u4e3a&#8221;\u8fc7\u534a\u6570\/\u591a\u6570\u51b3\u5b9a&#8221;\uff0c\u5f88\u591a\u4eba\u7ecf\u5e38\u7406\u89e3\u4e3a&#8221;Quorum\uff1f\u554a\uff0c\u662f\u6307\u591a\u6570\u51b3\u5b9a\/\u8fc7\u534a\u6570\u7684\u4e8b\u60c5\u5427\uff1f&#8221;\u3002<\/p>\n<p>\u534a\u6570\u4ee5\u4e0a\u7684\u8282\u70b9\u5b8c\u6210\u4e86\u57fa\u4e8e\u4e00\u81f4\u6027\u7684\u590d\u5236\u5b9e\u73b0\uff0c\u5177\u4f53\u5982\u4e0b\u6240\u793a\u3002<\/p>\n<p>\u4f7f\u7528\u8fc7\u534a\u6570\/\u591a\u6570\u51b3\u6765\u7ba1\u7406\u590d\u5236\u54c1\u7684\u65b9\u6cd5\uff1a<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">\u66f8\u8fbc\u6642: \u904e\u534a\u65701\u4ee5\u4e0a\u306e\u30ce\u30fc\u30c9\u306b\u3001\u30bf\u30a4\u30e0\u30b9\u30bf\u30f3\u30d72\u4ed8\u304d\u3067\u66f8\u8fbc\u3081\u308b\u307e\u3067\u5f85\u3064<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\u8aad\u8fbc\u6642: \u904e\u534a\u6570\u306e\u30ce\u30fc\u30c9\u304b\u3089\u8907\u88fd\u3092\u8aad\u307f\u8fbc\u3093\u3067\u3001\u4e00\u756a\u65b0\u3057\u3044\u30bf\u30a4\u30e0\u30b9\u30bf\u30f3\u30d7\u306e\u3082\u306e\u3092\u30af\u30e9\u30a4\u30a2\u30f3\u30c8\u306b\u8aad\u8fbc\u7d50\u679c\u3068\u3057\u3066\u8fd4\u3059<\/ul>\n<p>\u8fd9\u6837\u505a\u53ef\u4ee5\u4fdd\u8bc1\u5728\u8bfb\u5199\u4efb\u4f55\u4e00\u79cd\u60c5\u51b5\u4e0b\u90fd\u80fd\u201c\u786e\u4fdd\u201d\u83b7\u53d6\u5230\u6700\u65b0\u7684\u65f6\u95f4\u6233\u6570\u636e\uff0c\u540c\u65f6\u9700\u8981\u8fdb\u884c\u53e6\u5916\u4e00\u79cd\u5904\u7406\u624d\u80fd\u8fdb\u884c\u591a\u4e2a\u540c\u65f6\u5199\u5165\u3002<\/p>\n<p>\u7136\u800c\uff0c\u5149\u662f\u9019\u6a23\u4e00\u500b\u540d\u7a31\u300cQuorum\u300d\u5c31\u4ee3\u8868\u904e\u534a\u6578\/\u591a\u6578\u6c7a\u9019\u4e00\u6982\u5ff5\uff0c\u8b93\u6211\u4e0d\u7981\u731c\u60f3\u5176\u4e2d\u5fc5\u6709\u6240\u7570\uff0c\u65bc\u662f\u9019\u6b21\u6211\u505a\u4e86\u4e00\u4e9b\u7814\u7a76\u3002<\/p>\n<h1>\u5bf9\u4e8e\u8fd9\u6b21\u8c03\u67e5\u7684\u8d44\u6599<\/h1>\n<p>\u7ecf\u8fc7\u5404\u79cd\u8c03\u67e5\u7814\u7a76\uff0c\u4e0b\u9762\u7684\u8bfe\u7a0b\u7b2c7\u8282\u7cbe\u786e\u800c\u5b8c\u6574\u5730\u603b\u7ed3\u4e86\u3002\u56e0\u6b64\uff0c\u6211\u5c06\u5176\u4f5c\u4e3a\u4e3b\u8981\u8d44\u6599\u8fdb\u884c\u603b\u7ed3\u3002<\/p>\n<p>\u5206\u6563\u8ba1\u7b97\u539f\u7406\uff082003\u5e74\u590f\u5b63\uff09<br \/>\n\uff08\u745e\u58eb\u8054\u90a6\u5de5\u79d1\u5927\u5b66\u82cf\u9ece\u4e16\u5206\u6821\uff08ETH Zurich\uff09\u5206\u5e03\u5f0f\u8ba1\u7b97\u7814\u7a76\u7ec4\u5f00\u8bbe\u7684\u8bfe\u7a0b\uff09<\/p>\n<h1>\u4ec0\u4e48\u662fQuorum\uff1f<\/h1>\n<p>\u9996\u5148\u4ece\u5b9a\u4e49\u7684\u89d2\u5ea6\u5f00\u59cb\u3002<\/p>\n<p>\u5047\u8bbe\u6709\u4e00\u4e2a\u8282\u70b9\u96c6\u5408$V = \\{ v_1, v_2, &#8230;, v_n \\}$\u3002\u6211\u4eec\u79f0\u5305\u542b\u5728$V$\u4e2d\u7684\u5b50\u96c6\u5408\u7684\u96c6\u5408$\\mathcal{S} \\subset 2^V$\u4e3a\u4e00\u4e2a\u62dc\u5360\u5ead\u5171\u8bc6\u7cfb\u7edf\uff0c\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\u3002\u62dc\u5360\u5ead\u5171\u8bc6\u7cfb\u7edf\u7684\u5143\u7d20\u88ab\u79f0\u4e3a\u51b3\u8bae\u3002<\/p>\n<ul class=\"post-ul\">\u3069\u306e\uff12\u3064\u306equorum $Q_1, Q_2$\u3082\u5171\u901a\u90e8\u5206\u3092\u6301\u3064($Q_1 \\cap Q_2 \\neq \\emptyset$)<\/ul>\n<p>\u6211\u660e\u767d\u4e86\uff0c\u8fd9\u4e2a\u96c6\u5408\u96c6\u5408\u786e\u5b9e\u6210\u4e3a\u4e86\u8fd9\u4e2a\u4ef2\u88c1\u7cfb\u7edf\uff0c\u5176\u4e2d\u5305\u62ec\u4e86\u5177\u6709\u7edd\u5927\u591a\u6570\u5927\u5c0f\u7684\u8282\u70b9\u7684\u96c6\u5408\u3002<\/p>\n<p>\u5373\u4f7f\u4e0d\u8fbe\u5230\u8fc7\u534a\u6570\uff0c\u53ea\u8981\u662f\u4f7f\u7528\u4e86\u6cd5\u5b9a\u4eba\u6570\u5236\u5ea6\uff0c\u5c31\u4e00\u5b9a\u4f1a\u5728\u6cd5\u5b9a\u4eba\u6570\u4e4b\u95f4\u5b58\u5728\u5171\u540c\u90e8\u5206\uff0c\u56e0\u6b64\u53ef\u4ee5\u7528\u4ee5\u4e0b\u65b9\u5f0f\u5bf9\u4f7f\u7528\u8fc7\u534a\u6570\u7684\u65b9\u6cd5\u8fdb\u884c\u6cdb\u5316\u3002<\/p>\n<h2>\u4f7f\u7528Quorum\u7cfb\u7edf\u6765\u7ba1\u7406\u590d\u5236\u3002<\/h2>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">read\u3068write\u3067\u5171\u901a\u306equorum system\u3092\u5b9a\u7fa9\u3059\u308b<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\u66f8\u8fbc\u6642,\u8aad\u8fbc\u6642\u306b\u306f\u305d\u306e\u4e2d\u304b\u3089quorum\u3092\u4e00\u500b\u9078\u3093\u3067\u3001quorum\u306b\u6240\u5c5e\u3059\u308b\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u306b\u66f8\u8fbc\/\u8aad\u8fbc\u51e6\u7406\u3092\u884c\u3046(\u3069\u308c\u304b\u4e00\u500b\u3067\u3082\u5931\u6557\u3057\u305f\u3089\u30a8\u30e9\u30fc\u3068\u3059\u308b)<\/ul>\n<p>\u4f7f\u7528\u76f8\u540c\u7684quorum\u7cfb\u7edf\u8fdb\u884c\u8bfb\u53d6\u548c\u5199\u5165\u662f\u5173\u952e\u3002\u56e0\u6b64\uff0c\u5373\u4f7f\u6bcf\u6b21\u5199\u5165\/\u8bfb\u53d6\u5904\u7406\u9009\u62e9\u7684quorum\u4e0d\u540c\uff0c\u4e5f\u4e00\u5b9a\u4f1a\u5305\u542b\u91cd\u590d\u7684\u8282\u70b9\uff0c\u4ece\u800c\u53ef\u4ee5\u8bfb\u53d6\u5230\u6700\u65b0\u7684\u6570\u636e\u3002<\/p>\n<p>\u53ea\u8981\u5728\u6240\u6709\u8282\u70b9\u4e2d\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a\u6cd5\u5b9a\u4eba\u6570\u4ecd\u7136\u5b58\u5728\uff0c\u6570\u636e\u5c06\u4f1a\u88ab\u4fdd\u7559\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5373\u4f7f\u6709\u4e00\u534a\u4ee5\u4e0b\u7684\u8282\u70b9\u53d1\u751f\u6545\u969c\u505c\u6b62\uff0c\u7cfb\u7edf\u4ecd\u5c06\u6301\u7eed\u63d0\u4f9b\u6570\u636e\u3002<\/p>\n<h2>\u4f7f\u7528Quorum System\u5b9e\u73b0\u5206\u5e03\u5f0f\u9501\u3002<\/h2>\n<p>\u4f7f\u7528\u5171\u8bc6\u7cfb\u7edf\uff0c\u53ef\u4ee5\u5b9e\u73b0\u5206\u5e03\u5f0f\u9501\u3002\u5b9e\u73b0\u65b9\u6cd5\u5f88\u7b80\u5355\u3002<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">quorum\u3092\u9078\u3093\u3067\u3001\u5404\u30ce\u30fc\u30c9\u304b\u3089\u9806\u306block\u3092\u5f97\u308b\u3002\u4e00\u3064\u3067\u3082lock\u304c\u5f97\u3089\u308c\u306a\u304b\u3063\u305f\u3089\u3001\u305d\u308c\u307e\u3067\u5f97\u3089\u308c\u305flock\u3092release\u3057\u3066\u3084\u308a\u76f4\u3059<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">release\u3059\u308b\u3068\u304d\u306flock\u3092\u5f97\u305f\u6642\u306equorum\u306e\u5168\u30ce\u30fc\u30c9\u306elock\u3092release\u3059\u308b<\/ul>\n<p>\u5728\u4e2d\u6587\u4e2d\uff0c\u53ea\u9700\u8981\u4e00\u500b\u9078\u9805\u4f86\u91cd\u65b0\u8a6e\u91cb\u9019\u53e5\u8a71\uff1a<br \/>\n\u53ea\u6709\u4e00\u4e2a\u9009\u62e9\u3002\u7136\u800c\uff0c\u5982\u679c\u6ca1\u6709\u5b9a\u4e49\u4ee5\u9501\u5b9a\u987a\u5e8f\u4e3a\u4f9d\u636e\uff0c\u800c\u4e14\u4e24\u4e2a\u4ee5\u4e0a\u7684quorum\u5b58\u5728\u5171\u540c\u90e8\u5206\uff0c\u5219\u53ef\u80fd\u4f1a\u53d1\u751f\u6b7b\u9501\uff0c\u56e0\u6b64\u9700\u8981\u6ce8\u610f\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u8003\u8651\u4e0b\u9762\u8fd9\u4e2aQuorum\u7cfb\u7edf\uff08$v_2, v_3$\u662f\u5171\u6709\u90e8\u5206\uff09\u3002<\/p>\n<p>$$V = \\{ v_1, v_2, v_3, v_4 \\}\\;,\\; \\mathcal{QS} = \\{Q_1=\\{v_1, v_2, v_3\\}, Q_2=\\{v_2, v_3 ,v_4\\}\\}$$ can be paraphrased in Chinese as:<\/p>\n<p>$$V = \\{ v_1, v_2, v_3, v_4 \\}\\;,\\; \\mathcal{QS} = \\{Q_1=\\{v_1, v_2, v_3\\}, Q_2=\\{v_2, v_3 ,v_4\\}\\}$$<\/p>\n<p>\u5316\u7b80\u4e3a\uff1a<br \/>\n$$V = \\{ v_1, v_2, v_3, v_4 \\}\\;,\\; \\mathcal{QS} = \\{Q_1=\\{v_1, v_2, v_3\\}, Q_2=\\{v_2, v_3 ,v_4\\}\\}$$<\/p>\n<p>\u5047\u8bbe\u9009\u62e9\u4e86Q1\u8fdb\u7a0b\u4ecev1\u5f00\u59cb\uff0c\u9009\u62e9\u4e86Q2\u8fdb\u7a0b\u4ecev4\u5f00\u59cb\u9006\u5e8f\u83b7\u53d6\u9501\u8fdb\u884c\u6267\u884c\u3002\u5982\u679c\u5728Q1\u83b7\u53d6\u4e86v2\u7684\u9501\u7684\u60c5\u51b5\u4e0b\u65e0\u6cd5\u83b7\u53d6v3\u7684\u9501\uff0c\u540c\u65f6Q2\u83b7\u53d6\u4e86v3\u7684\u9501\u7684\u60c5\u51b5\u4e0b\u65e0\u6cd5\u83b7\u53d6v2\u7684\u9501\uff0c\u90a3\u4e48\u5c31\u4f1a\u53d1\u751f\u6c38\u8fdc\u65e0\u6cd5\u8fdb\u884c\u7684\u60c5\u51b5\uff0c\u4e5f\u5c31\u662f\u53d1\u751f\u4e86\u6b7b\u9501\u3002\u4e3a\u4e86\u9632\u6b62\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\uff0c\u9700\u8981\u901a\u8fc7\u8282\u70b9\u7684ID\u7b49\u65b9\u5f0f\u4ee5\u4e00\u5b9a\u7684\u987a\u5e8f\u6765\u8fdb\u884c\u8bbf\u95ee\u3002<\/p>\n<p>\u901a\u8fc7\u6309\u7167\u4e00\u5b9a\u7684\u8bbf\u95ee\u987a\u5e8f\u83b7\u53d6\u9501\uff0c\u53ef\u4ee5\u907f\u514d\u6b7b\u9501\u7684\u53d1\u751f\u3002\u7136\u800c\uff0c\u8fd9\u4f1a\u5927\u5927\u964d\u4f4e\u83b7\u53d6\u9501\u7684\u6548\u7387\u3002\u4e3a\u4e86\u66f4\u9ad8\u6548\u5730\u64cd\u4f5c\uff0c\u8fd8\u6709\u5176\u4ed6\u65b9\u6cd5\u53ef\u4f9b\u9009\u62e9\uff08\u53c2\u8003&#8221;Theorem 19.8, Principles of Distributed Computing&#8221;\uff09\u3002<\/p>\n<h1>\u5171\u8bc6\u7cfb\u7edf\u6709\u5f88\u591a\u79cd\u3002<\/h1>\n<p>\u4f5c\u4e3a\u5171\u8bc6\u7cfb\u7edf\uff0c\u56e0\u4e3a\u53ea\u8981\u6c42\u201c\u4efb\u610f\u9009\u62e9\u90fd\u6709\u91cd\u590d\u201d\uff0c\u6240\u4ee5\u4e0d\u4ec5\u4ec5\u662f\u8fc7\u534a\u6570\uff0c\u8fd8\u53ef\u4ee5\u60f3\u51fa\u8bb8\u591a\u5176\u4ed6\u7684\u5171\u8bc6\u65b9\u6848\u3002<\/p>\n<p>\u53d1\u751f\u4e86\u8bb8\u591a\u4e8b\u60c5\u3002\u6211\u5c06\u4ece\u6587\u672c\u4e2d\u9010\u4e00\u4ecb\u7ecd\u3002<\/p>\n<h2>\u9996\u5148\u590d\u4e60\u4e00\u4e0b\uff1a\u8fc7\u534a\u6570\uff08Majority\uff09<\/h2>\n<p>$$ \\mathcal{Majority} = \\{ Q \\subseteq V\\;|\\;|Q| = \\lfloor n\/2\\rfloor+1 \\}$$<\/p>\n<p>$$ \\mathcal{Majority} = \\{ Q \\subseteq V\\;|\\;|Q| = \\frac{n}{2}+1 \\}$$<\/p>\n<p>$$ \\mathcal{Majority} = \\{ Q \\subseteq V\\;|\\;|Q| = \\text{\u5411\u4e0b\u53d6\u6574}(n\/2)+1 \\}$$<\/p>\n<p>$$ \\mathcal{Majority} = \\{ Q \\subseteq V\\;|\\;|Q| = \\text{\u53d6\u6574}(n\/2)+1 \\}$$<\/p>\n<p>$$ \\mathcal{Majority} = \\{ Q \\subseteq V\\;|\\;|Q| = \\text{\u4e0b\u53d6\u6574}(n\/2)+1 \\}$$<\/p>\n<p>\u53ef\u80fd\u53ef\u4ee5\u9009\u62e9\u8d85\u8fc7\u4e00\u534a\u7684\u96c6\u5408\uff0c\u4f46\u57fa\u4e8equorum\u7684\u6761\u4ef6\u662f\u5b83\u4eec\u90fd\u5e94\u8be5\u6709\u5171\u540c\u7684\u90e8\u5206\uff0c\u6240\u4ee5\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u4e00\u4e2a\u6700\u5c0f\u9700\u8981\u56db\u4e2a\u8282\u70b9\u7684quorum\u7cfb\u7edf\u5c31\u8db3\u591f\u4e86\u3002<\/p>\n<h2>\u660e\u663e\u7684Quorum: \u5355\u4f8b\u6a21\u5f0f(Singleton)<\/h2>\n<p>$$ \\mathcal{Singleton} = \\{ \\{ v_{\\cdot} \\} \\}$$<br \/>\n$$ \\mathcal{Singleton} = \\{ \\{ v_{\\cdot} \\} \\}$$<\/p>\n<p>\u8fd9\u662f\u4e00\u4e2a\u7531\u4e00\u4e2a\u8282\u70b9\u7ec4\u6210\u7684Quorum\u7cfb\u7edf\u3002\u4ece\u590d\u5236\u7ba1\u7406\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u65e0\u8bba\u6709\u591a\u5c11\u4e2a\u8282\u70b9\uff0c\u90fd\u5c06\u8bfb\u64cd\u4f5c\u96c6\u4e2d\u5728\u4e00\u4e2a\u7279\u5b9a\u7684\u8282\u70b9\u4e0a\u3002\u5c3d\u7ba1\u53ef\u80fd\u4e0d\u592a\u6709\u7528\uff0c\u4f46\u8fd9\u4e5f\u662f\u4e00\u79cd\u5b8c\u5907\u7684Quorum\u7cfb\u7edf\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u5c06\u4f1a\u5f15\u5165\u4e00\u4e2a\u6709\u8da3\u7684\u8bae\u5458\u5236\u5ea6\u3002<\/p>\n<h2>\u7f51\u683c<\/h2>\n<p>\u5f53\u8003\u8651\u8282\u70b9\u7684\u5927\u5c0f\u4e3a$V$\uff0c\u6ee1\u8db3$|V|=n$\u4e3a\u5e73\u65b9\u6570\uff08\u5373$\\sqrt{n}$\u662f\u4e00\u4e2a\u6574\u6570\uff09\u65f6\uff0c\u8282\u70b9\u53ef\u4ee5\u88ab\u5e03\u7f6e\u6210\u4e00\u4e2a\u6b63\u65b9\u5f62\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u4f1a\u6309\u7167\u4ee5\u4e0b\u65b9\u5f0f\u9009\u62e9\u6cd5\u5b9a\u4eba\u6570\uff08\u53ef\u4ee5\u8003\u8651\u4ece\u7b2c$i+1$\u884c\u5f00\u59cb\u7684\u5404\u79cd\u9009\u62e9\uff09\u3002<\/p>\n<p>$$ \\mathcal{Grid} = \\{\\;\\{ (i\\text{ row in total})\\cup (select\\; one\\; at\\; random\\; from\\; each\\; of\\; the\\; following\\; rows}) \\}\\;|\\; 1 \\leq i \\leq \\sqrt{n}\\; \\}$$<\/p>\n<p>$$\\mathcal{Grid} = \\{\\;\\{ (\u7b2ci\u884c\u5168\u90e8)\\cup (\u968f\u673a\u4ece\u7b2ci+1\u884c\u53ca\u4ee5\u4e0b\u9009\u62e9\u4e00\u4e2a)\\}\\;|\\;1 \\leq i \\leq \\sqrt{n}\\;\\}$$<\/p>\n<div><img decoding=\"async\" class=\"post-images\" title=\"\" src=\"https:\/\/cdn.silicloud.com\/blog-img\/blog\/img\/657d9144913a08637a6def60\/54-0.png\" alt=\"image\" \/><\/div>\n<p>\u4e0a\u9762\u662f\u5f53\u56fa\u5b9a\u6bcf\u4e00\u5217\u65f6\u5f97\u5230\u7684\u60c5\u51b5\uff0c\u4e0b\u9762\u662f\u5f53\u4ece\u6bcf\u4e00\u884c\u4e2d\u9009\u62e9\u4e00\u4e2a\u4e0d\u91cd\u590d\u7684\u5143\u7d20\u65f6\u5f97\u5230\u7684\u60c5\u51b5\u3002\u5173\u952e\u5728\u4e8e\u53d6\u51fa\u6240\u6709\u7684\u7b2ci\u884c\uff0c\u5728\u5176\u4ed6\u7684\u9009\u4e3e\u673a\u5236\u4e2d\uff0c\u81f3\u5c11\u4f1a\u9009\u62e9\u5230i\u884c\u4e2d\u7684\u4e00\u4e2a\u8282\u70b9\uff0c\u4ece\u800c\u6ee1\u8db3\u9009\u4e3e\u673a\u5236\u7684\u6761\u4ef6\u3002<\/p>\n<p>\u4e0b\u9762\u5c06\u4f1a\u63d0\u53ca\uff0c$\\mathcal{Grid}$ \u5177\u6709\u8f83\u5f31\u7684\u6297\u6545\u969c\u6027\u8d28\u3002\u4e0b\u9762\u6240\u8ff0\u7684B-\u7f51\u683c\u662f\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u800c\u8bbe\u8ba1\u7684\u3002<\/p>\n<h2>B-\u7f51\u683c (B-<\/h2>\n<p>B-\u7f51\u683c\u4e0e\u7f51\u683c\u7c7b\u4f3c\uff0c\u5c06\u8282\u70b9\u6392\u5217\u6210\u7f51\u683c\u72b6\u3002\u4ee4$|V|=n=d \\cdot h \\cdot r$\u3002\u7f51\u683c\u7684\u5f62\u72b6\u662f\u4e00\u4e2a $h \\cdot r$ \u884c $d$ \u5217\u7684\u957f\u65b9\u5f62\u3002\u884c\u88ab\u5206\u4e3a $h$ \u4e2a\u7ec4\uff08\u79f0\u4e3aband\uff09\uff0c\u6bcf\u4e2aband\u6709 $r$ \u884c\u3002\u6bcf\u4e2aband\u5185\u7684\u884c\u88ab\u79f0\u4e3aminicolumn\u3002<\/p>\n<div><img decoding=\"async\" class=\"post-images\" title=\"\" src=\"https:\/\/cdn.silicloud.com\/blog-img\/blog\/img\/657d9144913a08637a6def60\/59-0.png\" alt=\"image\" \/><\/div>\n<p>\u5728B-\u7f51\u683c\u4e2d\uff0cquorum\u7cfb\u7edf\u7684\u9009\u62e9\u5982\u4e0b\u6240\u793a\uff08\u53c2\u89c1\u4e0a\u56fe\uff09\u3002<\/p>\n<p>$$ \\mathcal{BGrid} = \\left\\{\\; \\left\\{\\text{\u4ece\u6574\u4f53\u4e2d\u9009\u62e9\u4e00\u4e2aminicolumn}\\right\\} \\cup \\left\\{\\text{\u4ece\u6bcf\u4e2aminicolumn\u4e2d\u9009\u62e9\u4e00\u4e2a\u8282\u70b9\uff0c\u5176\u4e2d\u53ea\u9009\u62e9\u7b2ci\u4e2aband\u7684\u8282\u70b9}\\right\\} \\; | \\; 1 \\leq i \\leq h \\right\\}$$<\/p>\n<p>\u6bcf\u4e2a\u9009\u533a\u90fd\u7c7b\u4f3c\u4e8e\u7f51\u683c\u7684\u884c\uff0c\u8986\u76d6\u4e86\u6240\u6709\u5217\uff0c\u800c\u4e14\u6bcf\u4e2a\u9009\u533a\u90fd\u5728\u6bcf\u4e2a\u5757\u4e2d\u5177\u6709\u8ff7\u4f60\u5217\uff0c\u56e0\u6b64\u4e00\u5b9a\u4f1a\u6709\u5171\u540c\u90e8\u5206\u3002<\/p>\n<h2>\u6709\u9650\u6295\u5f71\u5e73\u9762\uff08Finite Projective Plane: FPP\uff09<\/h2>\n<p>\u4e5f\u6709\u63d0\u51fa\u4e86\u4f7f\u7528\u5177\u6709\u66f4\u9ad8\u62bd\u8c61\u5ea6\u7684\u51e0\u4f55\u7279\u6027\u7684\u62bd\u8c61\u5171\u8bc6\u7cfb\u7edf\u7684\u5efa\u8bae\u3002\u8fd9\u4e2a\u7cfb\u7edf\u4f7f\u7528\u4e86\u88ab\u79f0\u4e3a\u6295\u5f71\u5e73\u9762\u7684\u7a7a\u95f4\u3002\u5728\u6211\u4eec\u5e38\u89c1\u7684\u5e73\u9762\u4e2d\uff0c\u5e73\u884c\u7684\u4e24\u6761\u76f4\u7ebf\u65e0\u8bba\u5982\u4f55\u4e5f\u65e0\u6cd5\u76f8\u4ea4\uff0c\u4f46\u5728\u6295\u5f71\u5e73\u9762\u8fd9\u6837\u7684\u7a7a\u95f4\u4e2d\uff0c\u4efb\u610f\u4e24\u6761\u76f4\u7ebf\u90fd\u5177\u6709\u76f8\u4ea4\u7684\u7279\u6027\uff0c\u8fd9\u662f\u4e00\u4e2a\u795e\u5947\u7684\u7a7a\u95f4\u3002<\/p>\n<p>\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u6295\u5f71\u5e73\u9762\u53ef\u4ee5\u901a\u8fc7\u201c\u70b9\u7684\u96c6\u5408\u201d\u3001\u201c\u7ebf\uff08\u70b9\u7684\u96c6\u5408\uff09\u7684\u96c6\u5408\u201d\u548c\u5b83\u4eec\u4e4b\u95f4\u7684\u8fde\u63a5\u5173\u7cfb\u6765\u5b9a\u4e49\uff0c\u5b83\u6307\u7684\u662f\u6ee1\u8db3\u4ee5\u4e0b\u4e09\u4e2a\u6027\u8d28\u7684\u7ec4\u5408\u3002<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">$k^2 + k + 1$\u500b\u306e\u70b9\u3068$k^2 + k + 1$\u500b\u306e\u7dda\u3092\u6301\u3064<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">\u5404\u7dda\u306f$k+1$\u500b\u306e\u70b9\u3092\u3082\u3061\u3001\u5404\u70b9\u306f$k+1$\u500b\u306e\u7dda\u306b\u5c5e\u3059<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">\u3069\u306e2\u3064\u306e\u7dda\u3082\u4e00\u70b9\u3060\u3051\u3092\u5171\u6709\u3059\u308b<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\u7570\u306a\u308b2\u70b9\u3092\u542b\u3080\u7dda\u306f\u305f\u3060\u4e00\u3064\u3067\u3042\u308b<\/ul>\n<p>\u6211\u5b8c\u5168\u6ca1\u6709\u4eb2\u8eab\u4f53\u9a8c\u3002\u8ba9\u6211\u4eec\u5728$k=2$\u65f6\u8bd5\u7740\u7406\u89e3\u4e00\u4e0b\u3002\u4e0b\u56fe\u662f$k$\u7b49\u7ea7\u4e3a2\u65f6\u79f0\u4e3a&#8221;Fano\u5e73\u9762&#8221;\u7684\u56fe\u5f62\u3002<\/p>\n<div><img decoding=\"async\" class=\"post-images\" title=\"\" src=\"https:\/\/cdn.silicloud.com\/blog-img\/blog\/img\/657d9144913a08637a6def60\/68-0.png\" alt=\"image\" \/><\/div>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0cquorum\u7cfb\u7edf\u662f\u6307\u7531\u7ebf\uff08\u7531\u4e09\u4e2a\u70b9\u7ec4\u6210\u7684\u96c6\u5408\uff09\u7ec4\u6210\u7684\u96c6\u5408\u3002\u5373\u4e0a\u56fe\u4e2d\u7684<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">\u4e09\u89d2\u5f62\u306e\u5404\u8fba<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">\u5404\u8fba\u306e\u4e2d\u70b9\u3068\u9802\u70b9\u3092\u7d50\u30763\u3064\u306e\u4e2d\u7dda<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\u5404\u8fba\u306e\u4e2d\u70b9\u3068\u63a5\u3059\u308b\u5185\u63a5\u5186(\u30b3\u30ec\u3082\u7dda\u3067\u3059)<\/ul>\n<p>\u4e0d\u7ba1\u627e\u54ea\u4e24\u6761\u7ebf\uff0c\u90fd\u80fd\u786e\u4fdd\u4e00\u5b9a\u6709\u4e00\u4e2a\u70b9\u662f\u5171\u4eab\u7684\u3002<\/p>\n<h1>Quorum\u7cfb\u7edf\u7684\u4f18\u7f3a\u70b9(\u8bc4\u4ef7\u6807\u51c6)\u3002<\/h1>\n<p>\u55ef\uff0c\u6211\u4e86\u89e3\u5230\u6709\u8bb8\u591a\u4e0d\u540c\u7684\u6cd5\u5b9a\u4eba\u6570\u3002\u4ece\u4f3c\u4e4e\u6ca1\u6709\u7528\u7684$\\mathcal{Singleton}$\uff0c\u5230\u5e38\u7528\u7684$\\mathcal{Majority}$\uff0c\u8fd8\u6709\u7f51\u683c\u5e03\u7f6e\u548c\u88ab\u79f0\u4e3a\u5c04\u5f71\u5e73\u9762\u7684\u590d\u6742\u4e00\u4e9b\u7684\u9009\u9879\u3002<\/p>\n<p>\u5728\u7814\u7a76&#8221;quorum system&#8221;\u65f6\uff0c\u5df2\u7ecf\u63d0\u51fa\u4e86\u51e0\u79cd&#8221;\u7528\u4e8e\u6bd4\u8f83quorum system\u7684\u5ea6\u91cf\u6807\u51c6&#8221;\u3002\u8ba9\u6211\u4eec\u6765\u786e\u8ba4\u8fd9\u4e9b\u5ea6\u91cf\u6807\u51c6\u7684\u5b9a\u4e49\uff0c\u5e76\u8fdb\u884c\u6bd4\u8f83\u6211\u4eec\u5728\u672c\u6587\u4e2d\u4ecb\u7ecd\u7684quorum system\u3002<\/p>\n<h2>\u8d1f\u8f7d<\/h2>\n<p>\u4ece\u76f4\u89c9\u4e0a\u6765\u8bf4\uff0c\u5c31\u662f\u6bcf\u4e2a\u8282\u70b9\u88ab\u8bbf\u95ee\u7684\u9891\u7387\u3002\u5b9a\u4e49\u672c\u8eab\u662f\u6839\u636e\u5bf9\u51b3\u7b56\u7b56\u7565$W$\u5bf9quorum\u7684\u8bbf\u95ee\u65b9\u5f0f\u800c\u53d8\u5316\u7684\u5b9a\u4e49\u3002<\/p>\n<p>\u5b9a\u4e49\uff1a\u5c06$W$\u4f5c\u4e3aquorum system $\\mathcal{Q}$\u4e0a\u7684\u6982\u7387\u5bc6\u5ea6\uff0c\u5219\u79f0\u4e4b\u4e3a\u8bbf\u95ee\u7b56\u7565(access strategy)\u3002$P_W(Q)$\u8868\u793a\u9009\u62e9\u8bbf\u95ee\u7b56\u7565$W$\u65f6\u8bbf\u95ee$Q$\u7684\u6982\u7387\u3002<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">$W$\u306b\u3088\u3063\u3066\u5c0e\u304b\u308c\u308b\u30ce\u30fc\u30c9 $v$ \u306eload $l_w(v)$\u3092\u4e0b\u8a18\u3067\u5b9a\u7fa9\u3059\u308b(\u542b\u307e\u308c\u308bquorum\u304c\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u78ba\u7387\u3092\u5168\u90e8\u8db3\u3059)\u3002<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">$$<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">l_W(v) = \\sum_{Q\\in\\mathcal{Q}, v\\in Q} P_W(Q)<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">$$<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">$W$\u306b\u3088\u3063\u3066\u5c0e\u304b\u308c\u308b quorum system $\\mathcal{Q}$\u306e load $L_W(\\mathcal{Q})$\u3092\u4e0b\u8a18\u3067\u5b9a\u7fa9\u3059\u308b(\u5e73\u305f\u304f\u8a00\u3048\u3070\u4e00\u756a load \u306e\u9ad8\u3044\u3082\u306e\u3092\u5168\u4f53\u306e load \u3068\u3059\u308b)\u3002<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">$$<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">L_W(\\mathcal{Q}) = \\max_{v \\in V} l_W(i)<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">$$<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">quorum system $\\mathcal{Q}$ \u306eload $L(\\mathcal{Q})$\u3092\u4e0b\u8a18\u3067\u5b9a\u7fa9\u3059\u308b(\u3059\u3079\u3066\u306e$W$\u306e\u4e2d\u3067\u6700\u5c0f\u3068\u306a\u308b load \u306e\u5024)<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">$$<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">L(\\mathcal{Q}) = \\min_{W} L_W(\\mathcal{Q})<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">$$<\/ul>\n<p>\u53c2\u8003: \u5171\u8bc6\u7cfb\u7edf\u7684\u8d1f\u8f7d\u4e0b\u754c\u662f$1\/\\sqrt{n}$\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u65e0\u8bba\u5982\u4f55\uff0c\u8d1f\u8f7d\u90fd\u65e0\u6cd5\u5c0f\u4e8e\u8fd9\u4e2a\u503c\u3002\u76f8\u53cd\uff0c\u5982\u679c\u80fd\u591f\u8fbe\u5230\u8fd9\u4e2a\u8d1f\u8f7d\u503c\uff0c\u5219\u53ef\u4ee5\u8bf4\u5b83\u5728\u8d1f\u8f7d\u65b9\u9762\u662f\u6700\u4f18\u7684\u3002<\/p>\n<h2>\u5f3a\u97e7\u6027<\/h2>\n<p>\u4ec0\u4e48\u662f\u57fa\u4e8e\u6cd5\u5b9a\u4eba\u6570\u5236\u5ea6\u7684\u6545\u969c\u5bb9\u5fcd\u5ea6\u6307\u6807\uff1f\u57fa\u4e8e\u6cd5\u5b9a\u4eba\u6570\u5236\u5ea6\u7684\u5bb9\u9519\u6027\u8981\u6c42\u662f\u6307\u5728\u6cd5\u5b9a\u4eba\u6570\u5185\u7684\u6240\u6709\u8282\u70b9\u90fd\u6b63\u5e38\u5de5\u4f5c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c\u6cd5\u5b9a\u4eba\u6570\u5185\u7684\u4efb\u4f55\u4e00\u4e2a\u8282\u70b9\u53d1\u751f\u6545\u969c\uff0c\u90a3\u4e48\u591a\u6570\u6cd5\u5b9a\u4eba\u6570\u548c\u5171\u540c\u90e8\u5206\u5c06\u4e0d\u590d\u5b58\u5728\uff0c\u5bfc\u81f4\u7cfb\u7edf\u65e0\u6cd5\u4fdd\u8bc1\u6b63\u5e38\u8fd0\u884c\u3002\u5f39\u6027\u5ea6\u6307\u6807\u5b9a\u4e49\u4e86\u5f53\u6709\u591a\u5c11\u8282\u70b9\u505c\u673a\u65f6\uff0c\u6240\u6709\u6cd5\u5b9a\u4eba\u6570\u90fd\u65e0\u6cd5\u4fdd\u6301\u6b63\u5e38\u7684\u5065\u5eb7\u72b6\u6001\u3002<\/p>\n<p>\u5b9a\u4e49\uff1a\u62dc\u5360\u5ead\u5bb9\u9519\u7cfb\u7edf $\\mathcal{Q}$ \u7684\u5f39\u6027 $R(\\mathcal{Q})$ \u662f\u6307\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\u7684\u6700\u5927 $f$\u3002\u5bf9\u4e8e $V$ \u4e2d\u7684\u4efb\u610f\u5305\u542b $f$ \u4e2a\u8282\u70b9\u7684\u5b50\u96c6 $F$\uff0c\u81f3\u5c11\u5b58\u5728\u4e00\u4e2a\u4e0e\u5176\u4e0d\u76f8\u4ea4\u7684\u62dc\u5360\u5ead\u8d5e\u6210\u96c6\u3002<\/p>\n<h2>\u6545\u969c\u53d1\u751f\u7684\u53ef\u80fd\u6027 (The likelihood of failure occurrence)<\/h2>\n<p>\u5f39\u6027\u662f\u6307\u4e00\u4e2a\u8282\u70b9\u80fd\u591f\u627f\u53d7\u591a\u5c11\u4e2a\u505c\u6b62\u6545\u969c\u8282\u70b9\u3002\u4f46\u662f\u73b0\u5728\u6539\u4e3a\u8003\u8651\u6982\u7387\u3002\u5f53\u8282\u70b9\u7684\u53ef\u9760\u6027\u4e3a$p$\u65f6\uff0cQuorum\u7cfb\u7edf\u7684\u6545\u969c\u6982\u7387\u88ab\u5b9a\u4e49\u4e3a\u4efb\u4f55Quorum\u5185\u5305\u542b\u505c\u6b62\u6545\u969c\u8282\u70b9\u7684\u6982\u7387\u3002<\/p>\n<p>\u5b9a\u4e49: \u5177\u6709\u6545\u969c\u6982\u7387$F_p(\\mathcal{Q})$\u7684\u51b3\u7b56\u7cfb\u7edf$\\mathcal{Q}$\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u5b9a\u4e49:<\/p>\n<p>$$<br \/>\nF_p(\\mathcal{Q}) = Pr[\\forall Q\\in\\mathcal{Q},\\, \\exists v\\in Q\\,s.t. v\\text{\u505c\u6b62\u6545\u969c}]<br \/>\n$$<\/p>\n<h2>\u5728\u672c\u6b21\u4ecb\u7ecd\u7684Quoroum System\u8fdb\u884c\u5bf9\u6bd4<\/h2>\n<p>\u8ba9\u6211\u4eec\u4f7f\u7528\u4e0a\u8ff0\u7684\u8d1f\u8f7d\u3001\u5f39\u6027\u548c\u6545\u969c\u6982\u7387\u8fd9\u4e9b\u6307\u6807\u6765\u6bd4\u8f83\u6211\u4eec\u5728\u672c\u8282\u4ecb\u7ecd\u7684quorum\u7cfb\u7edf\u3002\u867d\u7136\u8be6\u7ec6\u7684\u5206\u6790\u8bf7\u53c2\u8003\u300a\u5206\u5e03\u5f0f\u8ba1\u7b97\u539f\u7406\u300b\uff0c\u4f46\u603b\u7ed3\u6210\u8868\u683c\u5982\u4e0b\uff1a<\/p>\n<div>\n<div class=\"post-table\">quorum systemLoadResilienceFailure ProbabilitySingleton$1$$0$$1-p$Majority$&gt;1\/2$$&lt;n\/2$$e^{-\\Omega(n)} \\to 0$Grid$\\Theta(1\/\\sqrt{n})$ <strong>(\u6700\u9069)<\/strong>$\\Theta(\\sqrt{n})$$(1 \u2212 p^d)^d \\to 1$B-Grid<sup id=\"fnref5\"><a title=\"$d=\\sqrt{n}\\,,r=\\ln d\\,, 0\\leq (1-p) \\leq 1\/3$\u3068\u3057\u3066\u3044\u308b\" href=\"#fn5\">5<\/a><\/sup>$\\Theta(1\/\\sqrt{n})$ <strong>(\u6700\u9069)<\/strong>$\\Theta(\\sqrt{n})$$O(1\/n) \\to 0$FPP$\\Theta(1\/\\sqrt{n})$ <strong>(\u6700\u9069)<\/strong>$k \\sim \\Theta(\\sqrt{n})$$\\to 1$<\/div>\n<\/div>\n<p>Regarding how to read the table, intuitively&#8230;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">Load: \u30ce\u30fc\u30c9\u304c\u3069\u306e\u304f\u3089\u3044\u306e\u983b\u5ea6\u3067\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u304b \u2794 \u5c0f\u3055\u3044\u307b\u3069\u3088\u3044<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">Resilience: \u3069\u306e\u304f\u3089\u3044\u306e\u6545\u969c\u53f0\u6570\u307e\u3067\u8010\u3048\u3089\u308c\u308b\u304b \u2794 \u5927\u304d\u3044\u307b\u3069\u3088\u3044<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">Failure Probability: \u3069\u306e\u304f\u3089\u3044\u306e\u78ba\u7387\u3067quorum\u5168\u4f53\u304c\u4f7f\u3048\u306a\u304f\u306a\u308b\u304b \u2794 \u5c0f\u3055\u3044\u307b\u3069\u3088\u3044<\/ul>\n<p>\u6211\u5c06\u5206\u522b\u67e5\u770b\u5b83\u4eec\u3002<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">Singleton: 1\u500b\u3057\u304b\u30ce\u30fc\u30c9\u3092\u4f7f\u308f\u306a\u3044\u306e\u3067\u30c0\u30e1\u30c0\u30e1\u3067\u3059\u306d\u3002<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">Majority: Resilience\u304c\u307b\u307c\u534a\u6570\u306a\u306e\u3067\u304b\u306a\u308a\u9ad8\u3044\u3067\u3059\u3002$n$ \u304c\u5927\u304d\u304f\u306a\u3063\u305f\u6642\u306e\u6545\u969c\u7387\u3082\u307b\u307c0\u3078\u6f38\u8fd1\u3059\u308b\u306e\u3067\u3059\u304c\u3001Load\u304c $1\/2$ \u3068\u304b\u306a\u308a\u9ad8\u3081\u3067\u3059\u3002<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">Grid: Load\u306f\u6700\u9069\u3002Resilience\u3082Majority\u3068\u6bd4\u3079\u308b\u3068$\\sqrt{n}$\u3068\u5c0f\u3055\u3081\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u6545\u969c\u7387\u304c$n$\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u9023\u308c\u30661\u306b\u8fd1\u3065\u3044\u3066\u3057\u307e\u3046\u306e\u3067NG\u3067\u3059\u3002<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">B-Grid: Load, Resilience\u306fGrid\u3068\u540c\u3058\u3067\u3001\u6545\u969c\u7387\u30820\u3078\u6f38\u8fd1\u3057\u3066\u3044\u304f\u306e\u3067\u826f\u3055\u305d\u3046\u3067\u3059\u3002<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">FPP: Grid\u3068\u540c\u3058\u3067\u3059<\/ul>\n<p>\u6839\u636e\u4e0a\u8ff0\u8003\u8651\uff0c\u6211\u8ba4\u4e3a\u7a0d\u5fae\u7c97\u7565\u5730\u6765\u8bf4\uff0c\u5982\u679c\u7528\u25ef\u00d7\u4fee\u6539\u4e0a\u9762\u7684\u8868\u683c\uff0c\u53ef\u80fd\u4f1a\u53d8\u6210\u4e0b\u9762\u8fd9\u6837\u3002\u8fd9\u6837\u4f60\u5c31\u4f1a\u53d1\u73b0\uff0c\u6bd4\u591a\u6570\u6d3e\u66f4\u597d\u7684\u6cd5\u5b9a\u4eba\u6570\u5236\u5ea6\u4e5f\u662f\u5b58\u5728\u7684\u3002<\/p>\n<div>\n<div class=\"post-table\">quorum systemLoadResilienceFailure ProbabilitySingleton\u00d7\u00d7\u00d7Majority\u00d7\u25ce\u25efGrid\u25ce\u25ef\u00d7B-Grid<sup id=\"fnref5\"><a title=\"$d=\\sqrt{n}\\,,r=\\ln d\\,, 0\\leq (1-p) \\leq 1\/3$\u3068\u3057\u3066\u3044\u308b\" href=\"#fn5\">5<\/a><\/sup>\u25ce\u25ef\u25efFPP\u25ce\u25ef\u00d7<\/div>\n<\/div>\n<p>\u6839\u636e\u8fd9\u5f20\u8868\uff0cB-Grid\u770b\u8d77\u6765\u5f88\u597d\uff0c\u4f46B-Grid\u7684\u5c3a\u5bf8\u53d7\u5230\u9650\u5236\uff0c\u5206\u6790\u4e2d\u4e5f\u9700\u8981\u6ce8\u610f\u8282\u70b9\u5229\u7528\u7387\u5047\u8bbe\u4e0d\u8d85\u8fc71\/3\u8fd9\u4e00\u70b9\u3002<\/p>\n<p>\u5c31\u5b9e\u9645\u5e94\u7528\u800c\u8a00\uff0c\u4ece\u8fd9\u4e2a\u5217\u8868\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u5e7f\u6cdb\u4f7f\u7528Majority\u7684\u539f\u56e0\u662f\u53ef\u4ee5\u5f88\u597d\u5730\u7406\u89e3\u5176\u91cd\u8981\u6027\uff08\u5373\u4f7f\u8d1f\u8f7d\u76f8\u5bf9\u8f83\u5927\uff0c\u97e7\u6027\u4e5f\u5f88\u91cd\u8981\uff0c\u540c\u65f6\u901a\u8fc7\u4e3a\u8bfb\u5199\u64cd\u4f5c\u5206\u914d\u6743\u91cd\uff0cMajority\u7cfb\u7edf\u8fd8\u53ef\u4ee5\u8c03\u6574\u8bfb\u5199\u65f6\u7684\u8d1f\u8f7d\uff09\u3002<\/p>\n<h1>\u5176\u4ed6\u7684Quorum\u4eec<\/h1>\n<p>\u8fd9\u6b21\u63d0\u5230\u7684\u4ef2\u88c1\u7cfb\u7edf\u53ea\u662f\u57fa\u672c\u7684\u4e00\u4e9b\u3002\u9664\u4e86\u8fd9\u4e9b\u4e4b\u5916\uff0c\u8fd8\u6709\u8bb8\u591a\u4e0d\u540c\u673a\u5236\u7684\u4ef2\u88c1\u7cfb\u7edf\u88ab\u63d0\u51fa\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u76ee\u524d\u7684\u5171\u8bc6\u7cfb\u7edf\u6a21\u578b\u53ea\u8003\u8651\u4e86\u505c\u6b62\u6545\u969c\uff0c\u4f46\u5728\u5206\u5e03\u5f0f\u7cfb\u7edf\u4e2d\u88ab\u8ba4\u4e3a\u6700\u68d8\u624b\u7684\u62dc\u5360\u5ead\u6545\u969c\u4e5f\u88ab\u7814\u7a76\u51fa\u4e86\u4e00\u79cd\u5177\u6709\u62dc\u5360\u5ead\u5bb9\u9519\u6027\u8d28\u7684\u62dc\u5360\u5ead\u5171\u8bc6\u7cfb\u7edf\u3002<\/p>\n<p>\u5bf9\u4e8e\u7ecf\u5178\u7684Quorum System\u800c\u8a00\uff0c\u5fc5\u987b\u8981\u6c42\u6ca1\u6709\u4efb\u4f55\u7684\u4ea4\u96c6\u624d\u80fd\u8fdb\u884c\u3002\u4f46\u662f\uff0c\u4e5f\u6709\u4e00\u79cd\u88ab\u79f0\u4e3a\u6982\u7387\u6027\u51c6\u5219\u7cfb\u7edf\uff08Probabilistic Quorum System\uff09\u7684\u7814\u7a76\uff0c\u5b83\u5141\u8bb8\u51c6\u5219\u4e4b\u95f4\u4ee5\u4e00\u5b9a\u7684\u6982\u7387\u8fdb\u884c\u4ea4\u96c6\u3002<\/p>\n<p>\u8bf7\u53c2\u8003\u76f8\u5173\u6587\u732e\u4ee5\u83b7\u53d6\u66f4\u591a\u4fe1\u606f\u3002(\u6211\u5df2\u7ecf\u63d0\u4f9b\u4e86\u4e00\u4efd\u5305\u542b\u8f83\u65b0\u548c\u8fc7\u53bb\u7814\u7a76\u6210\u679c\u5f15\u7528\u7684\u8c03\u67e5\u8d44\u6599)<\/p>\n<h1>\u603b\u7ed3<\/h1>\n<p>\u5728NoSQL\u7b49\u5f00\u6e90\u8f6f\u4ef6\u548c\u4ea7\u54c1\u7684\u6570\u636e\u4e00\u81f4\u6027\u8bbe\u7f6e\u4e2d\u7ecf\u5e38\u542c\u5230\u7684\u5173\u952e\u8bcd\u662f&#8221;Quorum&#8221;\u3002\u4e00\u5f00\u59cb\u6211\u7b80\u5355\u5730\u5c06\u5176\u7406\u89e3\u4e3a&#8221;\u591a\u6570\u51b3\/\u8fc7\u534a\u6570&#8221;\uff0c\u4f46\u5728\u8fdb\u4e00\u6b65\u8c03\u67e5\u540e\u53d1\u73b0\u5176\u5b9e\u975e\u5e38\u590d\u6742\uff0c\u7406\u89e3\u548c\u63d0\u53ca&#8221;Quorum\u5c31\u662f\u591a\u6570\u51b3&#8221;\u53ea\u662f\u51b0\u5c71\u4e00\u89d2\uff0c\u66f4\u6df1\u5c42\u6b21\u7684\u4e86\u89e3\u9700\u8981\u4e86\u89e3Quorum System\u8fd9\u4e2a\u7cfb\u7edf\uff0c\u540c\u65f6\u6211\u4e5f\u610f\u8bc6\u5230\u5728\u8003\u8651\u5206\u5e03\u5f0f\u7cfb\u7edf\u7684&#8221;\u64cd\u4f5c\u4fdd\u8bc1&#8221;\u65b9\u9762\uff0cQuorum\u662f\u4e00\u4e2a\u975e\u5e38\u5f3a\u5927\u7684\u5de5\u5177\u3002<\/p>\n<p>\u5b66\u4e60\u9664\u8fc7\u534a\u6570\u4e4b\u5916\u7684Quorum\u540e\uff0c\u4e0e\u7b80\u5355\u660e\u4e86\u7684\u8fc7\u534a\u6570\u591a\u7684Quorum\u76f8\u6bd4\uff0c\u867d\u7136\u8d1f\u8f7d\u66f4\u91cd\uff0c\u4f46\u5728\u5f39\u6027\u548c\u6545\u969c\u6982\u7387\u4e0a\u66f4\u4e3a\u4f18\u8d8a\u3002\u6b64\u5916\uff0c\u5728B-Grid\u4e2d\uff0c\u5c3d\u7ba1\u5b58\u5728\u89e3\u6790\u4e0a\u7684\u6280\u672f\u6027\u65b9\u9762\uff0c\u4f46\u4ece\u6e10\u8fd1\u89d2\u5ea6\u6765\u770b\uff0c\u5b83\u4f3c\u4e4e\u6bd4\u591a\u6570\u6d3e\u66f4\u597d\u3002<\/p>\n<p>\u5982\u679c\u8fd9\u7bc7\u6587\u7ae0\u80fd\u5e2e\u52a9\u5927\u5bb6\u66f4\u597d\u5730\u7406\u89e3&#8221;Quorum System&#8221;\uff0c\u6211\u4f1a\u611f\u5230\u975e\u5e38\u5e78\u798f\u3002<\/p>\n<h1>\u53c2\u8003\u8d44\u6599<\/h1>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">&#8220;The Origin of Quorum Systems&#8221;, Marko Vukoli\u0107, 2010<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul class=\"post-ul\">\n<li style=\"list-style-type: none;\">\n<ul class=\"post-ul\">&#8220;Selected Results from the Latest Decade of Quorum Systems Research&#8221;, Michael G. Merideth and Michael K. Reiter, 2010<\/ul>\n<\/li>\n<\/ul>\n<p>\u4eca\u56de\u53c2\u7167\u3057\u305f\u30c6\u30ad\u30b9\u30c8<\/p>\n<p>Principles of Distributed Computing<br \/>\nPrinciples of Distributed Computing (Summer 2003)<\/p>\n<div>\n<p>Cassandra\u548cRiak\u53ef\u4ee5\u5206\u522b\u8bbe\u7f6e\u8bfb\u53d6\u548c\u5199\u5165\u7684Quorum\u5927\u5c0f\uff0c\u4ee5\u6839\u636e\u6570\u636e\u7684\u8bfb\u53d6\/\u5199\u5165\u7279\u6027\u8fdb\u884c\u6027\u80fd\u8bbe\u7f6e\u3002<\/p>\n<p>\u65f6\u95f4\u6233\u901a\u5e38\u7528\u4e8e\u4e50\u89c2\u9501\u4e2d\uff0c\u4f7f\u7528\u5355\u8c03\u9012\u589e\u7684\u6570\u636e\u201c\u7248\u672c\u53f7\u201d\u3002<\/p>\n<p>\u6839\u636e\u94fe\u63a5\u4e2d\u63d0\u5230\u7684\u5185\u5bb9\uff0c\u7531\u4e8e\u8fd9\u662f2003\u5e74\u7684\u4fe1\u606f\uff0c\u8981\u5168\u9762\u5b66\u4e60\u6700\u65b0\u7684\u5206\u5e03\u5f0f\u7cfb\u7edf\u539f\u7406\uff0c\u6700\u597d\u4f7f\u7528\u73b0\u884c\u7248\u672c\u3002\u4ec5\u6bd4\u8f83Quorum\u7cfb\u7edf\u7684\u8bdd\uff0c2003\u5e74\u7684\u6587\u672c\u4ecb\u7ecd\u4e86\u8f83\u591a\u79cd\u7c7b\u7684Quorum\u7cfb\u7edf\uff0c\u56e0\u6b64\u672c\u6587\u9009\u62e9\u4e86\u8be5\u7248\u672c\u3002\u63d2\u5165\u7684\u56fe\u8868\u662f\u6839\u636e\u60c5\u51b5\u9009\u62e9\u6700\u6613\u7406\u89e3\u7684\u53c2\u8003\u3002<\/p>\n<p>&#8220;\u5fc5\u8981\u6700\u5c0f\u9650&#8221;\u8fd9\u4e00\u8868\u8fbe\u610f\u5473\u7740\u65e0\u8bba\u91c7\u53d6\u54ea\u4e24\u4e2aQuorum\uff0c\u5b83\u4eec\u90fd\u4e0d\u4f1a\u76f8\u4e92\u5305\u542b\u3002\u8fd9\u79cdQuorum\u7cfb\u7edf\u88ab\u79f0\u4e3a\u6700\u5c0fQuorum\u7cfb\u7edf\u3002<\/p>\n<p>\u5176\u4e2d$d=\\sqrt{n}\\,,r=\\ln d\\,, 0\\leq (1-p) \\leq 1\/3$\u3002<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u6700\u8fd1\uff0c&#8221;Quorum&#8221;\u8fd9\u4e2a\u8bcd\u53d8\u5f97\u5e76\u4e0d\u7f55\u89c1\u4e86\u3002\u5728\u7c7b\u4f3cZookeeper\u3001etcd\u3001Ser [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-50444","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.5 (Yoast SEO v21.5) - 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