{"id":57,"date":"2026-02-24T07:48:45","date_gmt":"2026-02-23T23:48:45","guid":{"rendered":"http:\/\/47.108.62.170\/?p=57"},"modified":"2026-04-15T01:22:20","modified_gmt":"2026-04-14T17:22:20","slug":"megiddo%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/okb385.org.cn\/index.php\/2026\/02\/24\/megiddo%e6%96%b9%e6%b3%95\/","title":{"rendered":"\u6700\u4f18\u6bd4\u7387\u751f\u6210\u6811"},"content":{"rendered":"\r\n<p class=\"wp-block-paragraph\">\u7ed9\u5b9a\u56fe$G=(V,E,c,p)$\uff0c\u5176\u4e2d$c: E(G)\\to \\R,p: E(G)\\to \\R_+$\uff0c\u6c42\u4e00\u4e2a$G$\u7684\u751f\u6210\u6811$T$\uff0c\u4f7f\u5f97<\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mfrac><mrow><msub><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>e<\/mi><mo>\u2208<\/mo><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>T<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msub><mi>c<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>e<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><msub><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>e<\/mi><mo>\u2208<\/mo><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>T<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msub><mi>p<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>e<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{\\sum_{e\\in E(T)}c(e)}{\\sum_{e\\in E(T)}p(e)}<\/annotation><\/semantics><\/math><\/div>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u6700\u5c0f\u3002<\/p>\r\n\r\n\r\n<!--more-->\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u8003\u8651Kruskal\u7684Megiddo\u65b9\u6cd5\uff0c\u8bbe\u6700\u4f18\u89e3\u662f$\\lambda^*$\u3002\u6211\u4eec\u5b9a\u4e49\u65b0\u8d39\u7528$c&#8217;=c-\\lambda^*p$\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5728Kruskal\u6700\u5f00\u59cb\u7684\u6392\u5e8f\u65f6\uff0c\u6bcf\u6b21\u9047\u5230$c&#8217;_i\\overset{?}{&lt;}c_j&#8217;$\u65f6\uff0c\u5176\u5b9e\u662f\uff1a<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\\[<br>\\frac{c(e_i)-c(e_j)}{p(e_i)-p(e_j)}\\overset{?}{&lt;}\\lambda^*<br>\\]<br><\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u628a\u5de6\u8fb9\u8fd9\u4e2a\u5206\u5f0f\u8bbe\u4e3a$\\lambda$\u5b9a\u4e49\u65b0\u8d39\u7528\uff0c\u8c03\u7528Kruskal\u770b\u8fd9\u4e2a\u8d39\u7528\u4e0b\u7684\u6700\u5c0f\u751f\u6210\u6811\u5927\u5c0fM\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5982\u679c$M&lt; 0$\uff0c\u8bf4\u660e$\\lambda$\u592a\u5927\u4e86\uff0c\u6700\u4f18\u6bd4\u503c$\\lambda^*$\u5e94\u8be5\u66f4\u5c0f\uff08\u56e0\u4e3a\u6700\u4f18\u6bd4\u7387\u53d6\u5230\u7684\u751f\u6210\u6811\u5927\u5c0f\u662f0\uff0c\u8c03\u5c0f\u8c03\u5927\u53c2\u6570\u4f1a\u8ba9\u6240\u6709\u751f\u6210\u6811\u7684\u5927\u5c0f\u90fd\u540c\u65f6\u6309\u4e0d\u540c\u6bd4\u7387\u589e\u5927\u6216\u7f29\u5c0f\uff0c\u5982\u679c$\\lambda$\u6bd4\u6700\u4f18\u6bd4\u7387\u5927\uff0c\u7b97\u51fa\u7684\u6700\u5c0f\u751f\u6210\u6811\u7684M\u4e5f\u4e00\u5b9a\u6bd40\u5c0f\uff09<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">$M> 0$\u7c7b\u4f3c\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u4e8e\u662f\u6bcf\u6b21\u8c03\u7528Kruskal\u4f5c\u4e3a\u9884\u8a00\u673a\u5f97\u5230\u65b0\u8d39\u7528\u5728\u6700\u4f18\u6bd4\u503c\u4e0b\u7684\u6392\u5e8f\u7ed3\u679c\uff0c\u5373\u4f7f\u6211\u4eec\u5c1a\u4e0d\u77e5\u9053$\\lambda^*$\u7684\u5b9e\u9645\u503c\uff0c\u7136\u540e\u6309\u8fd9\u4e2a\u7ed3\u679c\u518d\u8c03\u7528\u4e00\u6b21Kruskal\u5373\u53ef\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u603b\u590d\u6742\u5ea6$O(m\\log m\\cdot m\\alpha(n))\\approx O(m^2\\log n)$<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\u7ed9\u5b9a\u56fe$G=(V,E,c,p)$\uff0c\u5176\u4e2d$c: E(G)\\to \\R,p: E(G)\\to \\R_+$\uff0c\u6c42\u4e00\u4e2a$ [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","footnotes":""},"categories":[4,3,5],"tags":[38,39,37],"class_list":["post-57","post","type-post","status-publish","format-standard","hentry","category-4","category-3","category-5","tag-kruskal","tag-megiddo","tag-37"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - 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