{"id":1727,"date":"2021-12-11T23:35:42","date_gmt":"2021-12-11T15:35:42","guid":{"rendered":"https:\/\/ykyi.net\/?p=1727"},"modified":"2021-12-11T23:35:42","modified_gmt":"2021-12-11T15:35:42","slug":"fiduccia-mattheyses%e7%ae%97%e6%b3%95%e5%8d%b3fm%e7%ae%97%e6%b3%95%e7%9a%84%e8%ae%ba%e6%96%87%e8%a7%a3%e8%af%bb","status":"publish","type":"post","link":"https:\/\/ykyi.net\/?p=1727","title":{"rendered":"Fiduccia Mattheyses\u7b97\u6cd5(\u5373FM\u7b97\u6cd5)\u7684\u8bba\u6587\u89e3\u8bfb"},"content":{"rendered":"<p>kamuszhou\u7684\u535a\u5ba2\uff0c\u8f6c\u8f7d\u8bf7\u6ce8\u660eURL\u3002<\/p>\n<p>\u73b0\u4ee3\u5927\u89c4\u6a21\u96c6\u6210\u7535\u8def\u56fe\uff08VLSI\uff09\u975e\u5e38\u5e9e\u5927\uff0c\u5f53\u6211\u4eec\u5e0c\u671b\u7528\u591a\u4e2aFPGA\u4eff\u771f\u4e00\u4e2aVLSI\u65f6\uff0c\u9700\u8981\u628aVLSI\u5728\u6ee1\u8db3\u4e00\u4e9b\u7ea6\u675f\u6761\u4ef6\u7684\u60c5\u51b5\u4e0b\u5207\u5272\u6210\u591a\u4e2a\u5c0f\u90e8\u5206\uff0c\u6bcf\u4e2a\u90e8\u5206\u90fd\u53ef\u4ee5\u88c5\u8fdb\u4e00\u4e2aFPGA\u3002<\/p>\n<p>\u8fd9\u4e2a\u95ee\u9898\u62bd\u8c61\u6210\u6570\u5b66\u6a21\u578b\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u8d85\u56fe\u5206\u5272\u7684\u95ee\u9898\u3002\u5728\u8d85\u56fe\u5206\u5272\u9886\u57df\u6709\u4e00\u7bc7\u53d1\u8868\u4e8e1982\u5e74\u7684\u8bba\u6587\uff0c\u540d\u5b57\u662f&#8221;A Linear-Time Heuristic for Improving Network Partitions&#8221;\u3002\u8fd9\u7bc7\u8bba\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u6539\u8fdb\u7684\u201c\u8d85\u56fe\u4e8c\u5206\u95ee\u9898\u201d\u7b97\u6cd5\uff0c\u7b80\u79f0\u4e3aFM\u7b97\u6cd5\u3002\u867d\u7136\u57281982\u5e74\u8fd9\u7bc7\u8bba\u6587\u53d1\u8868\u65f6\uff0c\u201c\u8d85\u56fe\u5206\u5272\u201d\u7b97\u6cd5\u9886\u57df\u5df2\u7ecf\u53d1\u5c55\u4e86\u8fd1\u5341\u5e74\u3002\u4f46\u8fd9\u7bc7\u8bba\u6587\u4f3c\u4e4e\u6709\u7740\u8fd1\u4e4e\u7956\u5e08\u7237\u7ea7\u8bba\u6587\u7684\u5730\u4f4d\uff0c\u76f8\u5f53\u591a\u7684\u540e\u671f\u8be5\u9886\u57df\u7684\u8bba\u6587\u90fd\u4f1a\u5f15\u7528\u8fd9\u7bc7\u6587\u7ae0\u3002\u8bba\u6587\u53d1\u8868\u4e4b\u540e\u8be5\u9886\u57df\u7ee7\u7eed\u53d1\u5c55\u51fa\u7684\u201c\u5c42\u6b21\u5316\u8d85\u56fe\u591a\u5206\u5272\u201d\u7b97\u6cd5\u53ef\u4ee5\u770b\u6210\u662fFM\u7b97\u6cd5\u53d1\u5c55\u800c\u6765\u3002\u8be5\u7b97\u6cd5\u4e2d\u6d89\u53ca\u5230\u7684\u6982\u5ff5\u548c\u601d\u8def\u662f\u540e\u7eed\u7b97\u6cd5\u7684\u57fa\u7840\uff0c\u662f\u5f88\u597d\u7684\u8be5\u9886\u57df\u5165\u95e8\u5b66\u4e60\u7684\u8d44\u6599\u3002<br \/>\n\uff08\u66f4\u591a\u8d85\u56fe\u53ca\u8d85\u56fe\u5206\u5272\u7684\u57fa\u7840\u6982\u5ff5\u8bf7\u81ea\u884c\u641c\u7d22\uff0c\u672c\u535a\u5ba2\u4e3b\u8981\u89e3\u8bfb\u8bba\u6587\uff09<\/p>\n<p>\u8bba\u6587\u7684\u4e0b\u8f7d\u5730\u5740\uff1a<br \/>\n<a class=\"wp-editor-md-post-content-link\" href=\"https:\/\/ieeexplore.ieee.org\/document\/1585498\" title=\"https:\/\/ieeexplore.ieee.org\/document\/1585498\">https:\/\/ieeexplore.ieee.org\/document\/1585498<\/a><\/p>\n<p>\u5728\u8bba\u6587\u7684\u6458\u8981\u90e8\u5206\u8bba\u8ff0\u5230\uff1a\u672c\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u542f\u53d1\u5f0f\u7684\uff0c\u5229\u7528\u6700\u5c0f\u5272(mincut)\u7684\u8fed\u4ee3\u7b97\u6cd5\u89e3\u51b3\u8d85\u56fe\u4e8c\u5206\u95ee\u9898\u3002\u8be5\u7b97\u6cd5\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u662f\u7ebf\u6027\u7684\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u7edd\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u8be5\u7b97\u6cd5\u90fd\u53ea\u9700\u8981\u5f88\u5c11\u6b21\u6570\u7684\u8fed\u4ee3\u3002\u7b97\u6cd5\u6709\u4e09\u4e2a\u7279\u70b9\uff1a<br \/>\n1. \u8d85\u56fe\u88ab\u5206\u6210\u4e24\u4e2aBlock\u3002\u6bcf\u6b21\u79fb\u52a8\u4e00\u4e2a\u7ed3\u70b9\u628a\u5b83\u4ece\u539f\u6765\u7684Block\u79fb\u5f80\u53e6\u4e00\u4e2aBlock\u3002\u540c\u65f6\u7ef4\u6301\u4e24\u4e2aBlock\u7684\u5e73\u8861\u3002\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u4e2a\u5e73\u8861\u4e0d\u662f\u57fa\u4e8e\u6bcf\u4e2aBlock\u4e2d\u7684\u7ed3\u70b9\u6570\u91cf\uff0c\u800c\u662f\u66f4\u4e00\u822c\u7684size of block\u7684\u6982\u5ff5\uff0c\u5b83\u8003\u8651\u5230\u4e86\u6bcf\u4e2a\u7ed3\u70b9\u7684\u6743\u91cd\u662f\u4e0d\u4e00\u6837\u7684\u3002<br \/>\n2. \u5229\u7528\u4e00\u4e2a\u76f8\u5f53\u9ad8\u6548\u7684\u6570\u636e\u7ed3\u6784\uff0c\u53ef\u4ee5\u5728O(1)\u5e38\u6570\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u627e\u5230\u9700\u8981\u79fb\u52a8\u7684\u6700\u4f73\u7ed3\u70b9\u3002<br \/>\n3. \u5728\u79fb\u52a8\u4e86\u67d0\u4e2a\u7ed3\u70b9\u540e\uff0c\u518d\u9ad8\u6548\u5730\u66f4\u65b0\u53d7\u4e0a\u6b21\u79fb\u52a8\u5f71\u54cd\u7684\u7ed3\u70b9\u7684\u4fe1\u606f(\u5373\u8bba\u6587\u540e\u9762\u4f1a\u63d0\u5230\u7684\u7ed3\u70b9\u7684gain\u503c)\u3002\u8fd9\u7b2c\u4e09\u4e2a\u7279\u70b9\u4ea6\u5728\u8bba\u6587\u7684Introduction\u4e2d\u88ab\u518d\u6b21\u63d0\u5230\uff0c\u4f5c\u8005\u8ba4\u4e3a\u8fd9\u662f\u8be5\u8bba\u6587\u7684\u4e3b\u8981\u8d21\u732e(main contribution).<\/p>\n<h2>\u672f\u8bed\u53ca\u57fa\u672c\u6982\u5ff5<\/h2>\n<ul>\n<li>n(i): \u5f53i\u662f\u8d85\u8fb9\u7684\u7f16\u53f7\u65f6\uff0cn(i)\u5b9a\u4e49\u4e3a\u6bcf\u4e2a\u8d85\u8fb9\u4e0a\u7684\u7ed3\u70b9\u6570\u76ee\u3002<\/li>\n<li>s(i)\u6216p(i): \u5f53i\u8868\u793a\u7ed3\u70b9\u65f6\uff0cs(i)\u6216p(i)\u8868\u793a\u7ed3\u70b9\u4e0a\u7684PIN\u6570\u76ee\uff0c\u5373\u7ed3\u70b9\u4e00\u5171\u8ddf\u591a\u4e2a\u6761\u8d85\u8fb9\u6709\u8fde\u63a5\uff0c\u66f4\u591a\u65f6\u5019\u4ea6\u79f0\u4e3a\u7ed3\u70b9\u7684size\u3002<\/li>\n<li>\u90bb\u5c45\u7ed3\u70b9\uff1a \u5982\u679c\u4e24\u4e2a\u7ed3\u70b9\u81f3\u5c11\u80fd\u901a\u8fc7\u4e00\u6761\u8d85\u8fb9\u8fde\u63a5\uff0c\u5373\u4e3a\u90bb\u5c45\u7ed3\u70b9\u3002<\/li>\n<li>A\uff0cB\uff1a \u4ee3\u8868\u8d85\u56fe\u4e8c\u5206\u5272\u540e\u7684\u4e24\u4e2aBLOCK\u3002<\/li>\n<li>\uff5cA\uff5c\uff1a  <span class=\"katex math inline\">|A| = \\sum_{i=i}^{n}{s(i)}<\/span> \u5373Block A\u7684size\u5b9a\u4e49\u4e3aBlock A\u4e2d\u6240\u6709\u7684\u7ed3\u70b9\u7684size\u7684\u8fde\u52a0\u3002<\/li>\n<li>A(n)\u6216B(n)\uff1a n\u8868\u793a\u7f16\u53f7\u4e3an\u7684\u8fb9\uff0cA(n)\u5219\u8868\u793a\u8be5\u6761n\u5728Block A\u4e2d\u7684\u7ed3\u70b9\u6570\u3002<\/li>\n<li>cut: \u5728A\u548cB\u4e2d\u90fd\u6709\u7ed3\u70b9\u7684\u8d85\u8fb9\u3002<\/li>\n<li>cutstate: \u4e00\u6761\u8d85\u8fb9\u662f\u4e0d\u662fcut\uff08\u540e\u6765\u53d1\u5c55\u6210\u591a\u5206\u5272\u95ee\u9898\u4e2d\u7684cutsize\uff09\u3002<\/li>\n<li>cell gains: \u5f53\u79fb\u52a8\u4e00\u4e2a\u7ed3\u70b9\u5230\u53e6\u4e00\u4e2aBLOCK\u65f6\uff0ccut\u51cf\u5c11\u7684\u6570\u76ee\u3002<br \/>\n<img decoding=\"async\" src=\"http:\/\/supershell.cn\/wp-content\/uploads\/2021\/12\/cell_gains.png\" alt=\"cell gains\" \/><\/li>\n<\/ul>\n<h2>\u7ef4\u6301\u5e73\u8861<\/h2>\n<p>\u6700\u5bb9\u6613\u60f3\u5230\u7684\u662f\u5c31\u662f\u4f7f\u8d85\u56fe\u4e8c\u5206\u5272\u540e\u7684\u4e24\u4e2aBLOCK\u4e2d\u7684\u7ed3\u70b9\u6570\u91cf\u5927\u81f4\u76f8\u540c\u3002\u4e0d\u8fc7\uff0c\u53ef\u4ee5\u7a0d\u5fae\u53d8\u590d\u6742\u4e00\u70b9\uff0c\u5373\u8003\u8651\u6bcf\u4e2a\u7ed3\u70b9\u7684\u6743\u91cd\u3002<br \/>\n* W \uff1d |A| + |B|  \u6240\u6709\u7ed3\u70b9\u7684size\u8fde\u52a0\u548c<br \/>\n* r = |A| \/ (|A| + |B|)  \u4e00\u4e2a\u5927\u5c0f0\u52301\u4e4b\u95f4\u7684\u6bd4\u7387<br \/>\n* smax = <span class=\"katex math inline\">\\max_{1&lt;i&lt;n}{s(i)}<\/span>   \u6700\u5927\u7684\u7ed3\u70b9size<br \/>\n* rW &#8211; k \uff0a smax &lt;= |A| &lt;= rW + k * smax\uff1bk > 1  \u5e73\u8861\u516c\u5f0f<\/p>\n<p>\u516c\u5f0f\u4e0d\u96be\uff0c\u63cf\u8ff0\u5730\u5f88\u6e05\u695a\u3002\u7b80\u5355\u5730\u8bb2\uff0cblock\u7684size\u8003\u8651\u5230\u4e86\u6bcf\u4e2a\u7ed3\u70b9\u7684\u6743\u91cd\u4e0d\u540c\u3002\u53e6\u5916\uff0c\u5141\u8bb8\u6bcf\u4e2ablock\u7684size\u5728\u6ee1\u8db3\u6bd4\u7387r\u7684\u9644\u8fd1\u4e0a\u4e0b\u6d6e\u52a8k\u4e2a\u6700\u5927\u7ed3\u70b9size\u3002\u5b83\u7684\u542b\u4e49\u662f\uff0c\u5728\u521a\u597d\u6ee1\u8db3\u5206\u5272\u6bd4\u7387r\u7684\u65f6\u5019\uff0c\u8fd8\u80fd\u591f\u81f3\u5c11\u79fb\u52a8k\u4e2a\u7ed3\u70b9\u3002<\/p>\n<h2>\u7b97\u6cd5\u63cf\u8ff0<\/h2>\n<ol>\n<li>\u968f\u673a\u627e\u5230\u4e00\u4e2a\u5212\u5206A, B \uff08\u521d\u59cb\u5212\u5206\u5e76\u672a\u4e25\u683c\u8981\u6c42\u662f\u5728\u5e73\u8861\u72b6\u6001\uff09<\/li>\n<li>\u4eceA\u548cB\u4e2d\u90fd\u627e\u51fa\u5b83\u4eec\u5404\u81ea\u62e5\u6709\u6700\u9ad8gain\u503c\u7684\u7ed3\u70b9\uff0c\u5373\u6709\u4e24\u4e2a\u9884\u5907\u7ed3\u70b9\u3002<\/li>\n<li>\u6dd8\u6c70\u6389\u79fb\u52a8\u540e\u4f1a\u5bfc\u81f4\u4e0d\u5e73\u8861\u72b6\u6001\u51fa\u73b0\u7684\u9884\u5907\u7ed3\u70b9\u3002\u5982\u679c\u4e24\u4e2a\u9884\u5907\u7ed3\u70b9\u5747\u88ab\u6dd8\u6c70\uff0c\u5219\u7b97\u6cd5\u7ed3\u675f\u3002<\/li>\n<li>\u5728\u8fd9\u4e24\u4e2a\u7ed3\u70b9\u4e2d\u9009\u62e9\u62e5\u6709\u6700\u9ad8gain\u503c\u7684\u7ed3\u70b9\u79fb\u52a8\u5230\u5bf9\u7aef\u3002\u5982\u679c\u8fd9\u4e24\u4e2a\u9884\u5907\u7ed3\u70b9gain\u503c\u4e00\u6837\uff0c\u5c31\u9009\u4f1a\u5bfc\u81f4\u66f4\u597d\u5e73\u8861\u72b6\u6001\u7684\u7ed3\u70b9\u3002\u5982\u679c\u8fd8\u662f\u4e00\u6837\uff0c\u90a3\u5c31\u968f\u4f60\u7684\u5fc3\u60c5\u6311\u4e00\u4e2a(break ties as desired)\u3002<\/li>\n<li>\u9501\u5b9a\u8be5\u7ed3\u70b9\uff0c\u5728\u672c\u6b21\u8fed\u4ee3\u4e2d\u4e0d\u51c6\u518d\u4f7f\u7528\u3002<\/li>\n<li>\u66f4\u65b0\u5404\u4e2a\u7ed3\u70b9\u7684gain\u503c\uff0c\u8df3\u5230\u6b65\u9aa42\u7ee7\u7eed\u4e0b\u4e00\u6b21\u8fed\u4ee3\u3002<\/li>\n<\/ol>\n<h2>\u9ad8\u6548\u7684\u6570\u636e\u7ed3\u6784<\/h2>\n<p>FM\u7b97\u6cd5\u4e2d\u6709\u4e24\u4e2a\u96be\u70b9\uff0c\u5373\u5982\u4f55\u5feb\u901f\u627e\u5230\u6bcf\u4e2aBlock\u4e2dgain\u503c\u6700\u9ad8\u7684\u7ed3\u70b9\u4ee5\u53ca\u9ad8\u6548\u7684\u66f4\u65b0gain\u503c\u4ee5\u53cd\u5e94\u79fb\u52a8\u7ed3\u70b9\u5e26\u6765\u7684\u53d8\u5316\u3002\u7b2c\u4e00\u95ee\u9898\u7531\u4e0b\u56fe\u6240\u793a\u7684\u6570\u636e\u7ed3\u6784\u89e3\u51b3\u3002<br \/>\n<img decoding=\"async\" src=\"http:\/\/supershell.cn\/wp-content\/uploads\/2021\/12\/bucket_list_structure.png\" alt=\"data structures\" \/><\/p>\n<p>\u5982\u56fe\u7684\u6570\u636e\u7ed3\u6784\u5171\u6709\u4e24\u4e2a\u3002A\uff0cB\u4e24\u4e2aBLOCK\u5404\u6709\u4e00\u4e2a\u3002\u5176\u4e2d pmax\u5373\u6240\u6709\u7ed3\u70b9\u4e2d\u6700\u5927size\u3002\u663e\u7136\uff0c\u6bcf\u4e2a\u7ed3\u70b9\u7684gain\u503c\u90fd\u5728[-pmax, +pmax]\u4e4b\u95f4\u3002\u5f53pmax\u503c\u76f8\u5bf9\u8f83\u5c0f\u65f6\uff0c\u53ef\u4ee5\u7528\u4e00\u4e2a\u9759\u6001\u6570\u7ec4\u8868\u793a\u3002FM\u8bba\u6587\u4e2d\u5373\u7528\u9759\u6001\u6570\u7ec4\uff0c\u4f46\u540e\u6765VLSI\u6301\u7eed\u53d1\u5c55\uff0c\u9759\u6001\u6570\u7ec4\u592a\u5927\u7684\u65f6\u5019\uff0c\u5373\u53ef\u6362\u6210\u7528hash\u8868\u3002\u56fe\u4e2d\uff0c\u575a\u7740\u7684\u6570\u7ec4\u8868\u793a\u5728\u6bcf\u4e00\u4e2again\u503c\u4e0b\u9762\u7528\u94fe\u8868\u5b58\u653eFree\u7ed3\u70b9\uff0c\u5e76\u7528\u4e00\u4e2a\u6807\u8bb0\u8bb0\u5f55\u5f53\u524d\u6700\u9ad8gain\u503c\u662f\u591a\u5c11\u3002\u6a2a\u7740\u7684\u6570\u7ec4\u5219\u5b58\u653e\u4e86\u6240\u6709\u7684\u7ed3\u70b9\u3002\u8fd9\u6837\uff0c\u5c31\u80fd\u5728\u5e38\u6570\u65f6\u95f4\u5185\u627e\u5230\u6700\u5927\u7684gain\u503c\u548c\u4efb\u610f\u4e00\u4e2a\u7ed3\u70b9\u3002<\/p>\n<h2>\u9ad8\u6548\u5730\u66f4\u65b0gain\u503c<\/h2>\n<p>\u5f53\u4e00\u4e2a\u7ed3\u70b9\u4ece\u5f53\u524dBLOCK\u79fb\u5230\u5bf9\u7aefBLOCK\u540e\uff0c\u4f1a\u9020\u6210\u5b83\u7684\u6240\u6709\u90bb\u5c45\u7ed3\u70b9\u7684gain\u503c\u6709\u53ef\u80fd\u53d1\u751f\u53d8\u5316\u3002\u5982\u679c\u7528\u4e00\u4e2anaive\u7684\u7b97\u6cd5\uff0c\u6548\u7387\u4f1a\u5f88\u4f4e\u3002\u8bba\u6587\u4e2d\u8bba\u8ff0\u4e86naive\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6O(P^2)\uff0cP\u8868\u793a\u8d85\u56fe\u4e2d\u6240\u6709PIN\u7684\u603b\u6570\u76ee\u3002\u8fd9\u4e2a\u65f6\u95f4\u590d\u6742\u5ea6\u5f88\u5413\u4eba\uff0c\u4f46\u6211\u8ba4\u4e3a\u8fd9\u662f\u6700\u574f\u6781\u7aef\u60c5\u51b5\u4e0b\u3002\u4f46\u66f4\u8be6\u7ec6\u7684\u8bba\u8ff0\u8fd9\u91cc\u5c31\u7565\u8fc7\u5427\uff0c\u4e3b\u8981\u8bb2FM\u7b97\u6cd5\u662f\u600e\u4e48\u505a\u7684\uff0c\u8fd9\u662f\u8be5\u8bba\u6587\u4f5c\u8005\u6700\u5f97\u610f\u7684\u90e8\u5206\u3002<\/p>\n<p>\u5148\u5f15\u5165\u5173\u952e\u8fb9\u7684\u6982\u5ff5\u3002<br \/>\n<img decoding=\"async\" src=\"http:\/\/supershell.cn\/wp-content\/uploads\/2021\/12\/critical_nets.png\" alt=\"critical net\" \/><br \/>\n\u5f53\u4e14\u4ec5\u5f53A(n)\u6216B(n)\u7b49\u4e8e0\u6216\u8005\u7b49\u4e8e1\u65f6\uff0c\u4e00\u6761\u8fb9\u80fd\u79f0\u4e4b\u4e3a\u5173\u952e\u8fb9\u3002<\/p>\n<p>(kamuszhou\u7684\u535a\u5ba2\uff0c\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u6e90URL)<\/p>\n<h3>\u4e24\u4e2a\u91cd\u8981\u8bba\u8ff0\uff1a<\/h3>\n<ol>\n<li>\n<blockquote><p>\n  If the net is not critical, its cutstate cannot be affected by a move\n<\/p><\/blockquote>\n<p>\u5982\u679c\u4e00\u6761\u8fb9\u4e0d\u662f\u5173\u952e\u8fb9\uff0c\u90a3\u4e48\u4e0d\u53ef\u80fd\u53ea\u901a\u8fc7\u4e00\u6b21\u79fb\u52a8\u6539\u53d8\u8be5\u8fb9\u7684cutstate\u3002<\/p>\n<\/li>\n<li>\n<blockquote>\n<p>A net which is not critical either before or after a move cannot possibly influence the gains of any of its cells.\n<\/p><\/blockquote>\n<p>\u5982\u679c\u4e00\u6761\u8fb9\u5728\u79fb\u52a8\u524d\u548c\u79fb\u52a8\u540e\uff0c\u5b83\u90fd\u4e0d\u662f\u5173\u952e\u8fb9\uff0c\u90a3\u8fd9\u6761\u8fb9\u5219\u4e0d\u5f71\u54cdgain\u503c\u7684\u66f4\u65b0\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u90a3\u4e0d\u5c31\u662f\uff5e\uff5e\uff5e\uff5e<br \/>\n\u5982\u4f55\u66f4\u65b0gain\u503c\uff0c\u53ea\u7528\u7ba1\u79fb\u52a8\u524d\u662f\u5173\u952e\u8fb9\uff0c\u6216\u8005\u79fb\u52a8\u540e\u662f\u5173\u952e\u8fb9\u8fd9\u4e24\u79cd\u60c5\u51b5\u4e48\uff01\uff01\uff01<\/p>\n<p>\u8003\u5bdf\u4e00\u4e2a\u7ed3\u70b9\uff0c\u628a\u8be5\u7ed3\u70b9\u4eceFrom Block\u79fb\u52a8\u5230To Block\u8fd9\u4e2a\u79fb\u52a8\u524d\u540e\u7684\u72b6\u6001\u3002<br \/>\nF(n)\u5b9a\u4e49\u4e3a\u4e00\u6761\u8d85\u8fb9n\u5728From Block\u4e2d\u7684\u7ed3\u70b9\u6570\u3002<br \/>\nT(n)\u5b9a\u4e49\u4e3a\u4e00\u6761\u8d85\u8fb9n\u5728To Block\u4e2d\u7684\u7ed3\u70b9\u6570\u3002<br \/>\n\u79fb\u52a8\u524d\u7b26\u5408\u54ea\u4e9b\u6761\u4ef6\u7684\u8fb9\u662f\u8d85\u8fb9\u5462\uff1f<br \/>\nF(n) = 1 or T(n) = 0 or T(n) = 1 \u5176\u4e2dF(n) = 0\u8fdd\u53cd\u6761\u4ef6\uff0c\u4e0d\u5b58\u5728\u3002<br \/>\n\u79fb\u52a8\u540e\u54ea\u4e9b\u8fb9\u662f\u8d85\u8fb9\u5462\uff1f<br \/>\nT(n) = 1 or F(n) = 0 or F(n) = 1 \u5176\u4e2dT(n) = 0\u8fdd\u53cd\u6761\u4ef6\uff0c\u4e0d\u5b58\u5728\u3002<\/p>\n<p>\u518d\u5ea6\u60ca\u4eba\u5730\u53d1\u73b0\uff01\uff01\uff01<br \/>\n\u79fb\u52a8\u524d\u7684F(n) = 1 \u5373\u662f\u79fb\u52a8\u540e\u7684 F(n) = 0<br \/>\n\u79fb\u52a8\u524d\u7684T(n) = 0 \u5373\u662f\u79fb\u52a8\u540e\u7684 T(n) = 1<\/p>\n<p>\u4e8e\u662f\uff5e\uff5e\u7b26\u5408\u4ec0\u4e48\u6761\u4ef6\u7684\u8d85\u8fb9\u5c06\u5f71\u54cdgain\u503c\u7b80\u5316\u4e3a\uff1a<br \/>\n\u79fb\u52a8\u524d\u7b26\u5408\uff1a<br \/>\nT(n) = 0 or T(n) = 1<br \/>\n\u79fb\u52a8\u540e\u7b26\u5408\uff1a<br \/>\nF(n) = 0 or F(n) = 1<\/p>\n<p>\u4e8e\u662f\uff0c\u5f97\u5230\u7b97\u6cd5\uff1a<br \/>\n<img decoding=\"async\" src=\"http:\/\/supershell.cn\/wp-content\/uploads\/2021\/12\/updating_gains.png\" alt=\"udpate gains\" \/><\/p>\n<h2>\u672c\u6587\u672a\u5c3d\u7ec6\u8282<\/h2>\n<p>\u672c\u6587\u7701\u7565\u4e86\u5982\u4f55\u8ba1\u7b97\u6bcf\u4e2a\u7ed3\u70b9\u7684\u521d\u59cbgain\u503c\uff0c\u548c\u5982\u4f55\u751f\u6210\u521d\u59cb\u72b6\u6001\u7684\u6570\u636e\u7ed3\u6784\u3002\u56e0\u4e3a\u8fd9\u4e24\u4e2a\u7b97\u6cd5\u90fd\u76f8\u5bf9\u7b80\u5355\uff0c\u6240\u4ee5\u5c31\u7565\u8fc7\uff0c\u7740\u91cd\u4e8e\u8bba\u6587\u4f5c\u8005\u6700\u4e3a\u5f97\u610f\u7684\u9ad8\u6548\u66f4\u65b0gain\u503c\u7684\u90e8\u5206\u3002<\/p>\n<blockquote><p>\n  Our main contribution consists of an analysis of the effects a cell move has on its neighboring cells and a subsequent efficient implementaion of these results.\n<\/p><\/blockquote>\n<p>\u672c\u6587\u8fd8\u7701\u7565\u4e86\u8bba\u8005\u53d1\u73b0\u7684\u51e0\u4e2a\u547d\u9898(proposition)\uff0c\u53ca\u4e00\u4e9b\u7b97\u6cd5\u590d\u6742\u5ea6\u7684\u5206\u6790\u548c\u8bc1\u660e\u3002<\/p>\n<p>\u8fd8\u7701\u7565\u4e86\u5176\u4ed6\u7ec6\u8282\uff5e\u6700\u597d\u8fd8\u662f\u8bfb\u539f\u6587\uff01\u7ed9\u4f60\u4e0d\u4e00\u6837\u7684\u4e1d\u6ed1\u611f\u53d7\u3002<\/p>\n<h2>FM\u7b97\u6cd5\u7684\u7f3a\u70b9<\/h2>\n<p>\u5728\u53e6\u4e00\u7bc7\u8bba\u6587\u4e2d\uff0c\u63d0\u5230FM\u7b97\u6cd5\u76843\u4e2a\u7f3a\u70b9\u3002<br \/>\n1. \u5f53\u4e24\u8fb9Block\u9009\u51fa\u7684gain\u503c\u4e00\u6837\u65f6\uff0c\u7ed9\u7684\u5904\u7406\u65b9\u5f0f\u8fc7\u4e8e\u7b80\u5355\uff0c\u4e0d\u591f\u6709\u6d1e\u5bdf\u529b(insightful)\u3002<br \/>\n2. \u5f53\u4e00\u6761\u8d85\u8fb9\u5728\u4e24\u4e2aBlock\u4e2d\u7684\u7ed3\u70b9\u6570\u90fd\u5927\u4e8e\u6216\u7b49\u4e8e\u4e24\u4e2a\u65f6\uff0c\u5b83\u4eec\u5c31\u6ca1\u6709\u8d44\u683c\u5728\u7b2c\u4e00\u65f6\u95f4\u88ab\u9009\u4e3a\u5f85\u79fb\u52a8\u7ed3\u70b9\u3002\u8fd9\u663e\u7136\u592a\u8fc7greedy\u4e86\u3002<br \/>\n3. \u597d\u50cf\u8fd8\u63d0\u5230\u8fc7\u5176\u4ed6\u7f3a\u70b9\u4f46\u662f\u6211\u5fd8\u8bb0\u4e86\uff5e<\/p>\n<h2>\u8bfb\u540e\u611f<\/h2>\n<p>\u4e3a\u4f55\u5927\u4f6c\u90a3\u4e48\u5389\u5bb3\uff5e<br \/>\n\u4e00\u4e2a\u7ed3\u70b9\u7684\u79fb\u52a8\u5bf9\u5b83\u7684\u90bb\u5c45\u7ed3\u70b9gain\u503c\u7684\u5f71\u54cd\u7684\u5206\u6790\u786e\u5b9e\u76f8\u5f53\u4e4b\u7cbe\u5f69\u3002\u867d\u7136\u6ca1\u6709\u590d\u6742\u7684\u6570\u5b66\u516c\u5f0f\uff0c\u4f46\u540c\u6837\u903b\u8f91\u4e25\u8c28\uff0c\u62bd\u4e1d\u5265\u8327\u7684\u5206\u6790\u3002\u8ba9\u4eba\u62cd\u6848\u53eb\u7edd\uff5e<br \/>\n\u4e3a\u4f55\u4f5c\u8005\u80fd\u601d\u8003\u5f97\u8fd9\u4e48\u6709\u6761\u7406\u548c\u6df1\u5165\uff1f\uff1f<br \/>\n\u9664\u4e86\u5177\u4f53\u7684\u7b97\u6cd5\u672c\u8eab\uff0c\u8fd8\u80fd\u5b66\u5230\u54ea\u4e9b\u601d\u8003\u5206\u6790\u590d\u6742\u95ee\u9898\u7684\u65b9\u5f0f\u5462\uff1f<br \/>\n1. \u7b80\u5316\u95ee\u9898<br \/>\n2. \u63d0\u70bc\u89c4\u5f8b<\/p>\n<p>\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u51fa\u5904\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>kamuszhou\u7684\u535a\u5ba2\uff0c\u8f6c\u8f7d\u8bf7\u6ce8\u660eURL\u3002 \u73b0\u4ee3\u5927\u89c4\u6a21\u96c6\u6210\u7535\u8def\u56fe\uff08VLSI\uff09\u975e\u5e38\u5e9e\u5927\uff0c\u5f53\u6211\u4eec\u5e0c\u671b\u7528\u591a\u4e2aFPGA\u4eff\u771f\u4e00\u4e2aVLSI\u65f6\uff0c\u9700\u8981\u628aVLSI\u5728\u6ee1\u8db3\u4e00\u4e9b\u7ea6\u675f\u6761\u4ef6\u7684\u60c5\u51b5\u4e0b\u5207\u5272\u6210\u591a\u4e2a\u5c0f\u90e8\u5206\uff0c\u6bcf\u4e2a\u90e8\u5206\u90fd\u53ef\u4ee5\u88c5\u8fdb\u4e00\u4e2aFPGA\u3002 \u8fd9\u4e2a\u95ee\u9898\u62bd\u8c61\u6210\u6570\u5b66\u6a21\u578b\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u8d85\u56fe\u5206\u5272\u7684\u95ee\u9898\u3002\u5728\u8d85\u56fe\u5206\u5272\u9886\u57df\u6709\u4e00\u7bc7\u53d1\u8868\u4e8e1982\u5e74\u7684\u8bba\u6587\uff0c\u540d\u5b57\u662f&#8221;A Linear-Time Heuristic for Improving Network Partitions&#8221;\u3002\u8fd9\u7bc7\u8bba\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u6539\u8fdb\u7684\u201c\u8d85\u56fe\u4e8c\u5206\u95ee\u9898\u201d\u7b97\u6cd5\uff0c\u7b80\u79f0\u4e3aFM\u7b97\u6cd5\u3002\u867d\u7136\u57281982\u5e74\u8fd9\u7bc7\u8bba\u6587\u53d1\u8868\u65f6\uff0c\u201c\u8d85\u56fe\u5206\u5272\u201d\u7b97\u6cd5\u9886\u57df\u5df2\u7ecf\u53d1\u5c55\u4e86\u8fd1\u5341\u5e74\u3002\u4f46\u8fd9\u7bc7\u8bba\u6587\u4f3c\u4e4e\u6709\u7740\u8fd1\u4e4e\u7956\u5e08\u7237\u7ea7\u8bba\u6587\u7684\u5730\u4f4d\uff0c\u76f8\u5f53\u591a\u7684\u540e\u671f\u8be5\u9886\u57df\u7684\u8bba\u6587\u90fd\u4f1a\u5f15\u7528\u8fd9\u7bc7\u6587\u7ae0\u3002\u8bba\u6587\u53d1\u8868\u4e4b\u540e\u8be5\u9886\u57df\u7ee7\u7eed\u53d1\u5c55\u51fa\u7684\u201c\u5c42\u6b21\u5316\u8d85\u56fe\u591a\u5206\u5272\u201d\u7b97\u6cd5\u53ef\u4ee5\u770b\u6210\u662fFM\u7b97\u6cd5\u53d1\u5c55\u800c\u6765\u3002\u8be5\u7b97\u6cd5\u4e2d\u6d89\u53ca\u5230\u7684\u6982\u5ff5\u548c\u601d\u8def\u662f\u540e\u7eed\u7b97\u6cd5\u7684\u57fa\u7840\uff0c\u662f\u5f88\u597d\u7684\u8be5\u9886\u57df\u5165\u95e8\u5b66\u4e60\u7684\u8d44\u6599\u3002 \uff08\u66f4\u591a\u8d85\u56fe\u53ca\u8d85\u56fe\u5206\u5272\u7684\u57fa\u7840\u6982\u5ff5\u8bf7\u81ea\u884c\u641c\u7d22\uff0c\u672c\u535a\u5ba2\u4e3b\u8981\u89e3\u8bfb\u8bba\u6587\uff09 \u8bba\u6587\u7684\u4e0b\u8f7d\u5730\u5740\uff1a https:\/\/ieeexplore.ieee.org\/document\/1585498 \u5728\u8bba\u6587\u7684\u6458\u8981\u90e8\u5206\u8bba\u8ff0\u5230\uff1a\u672c\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u542f\u53d1\u5f0f\u7684\uff0c\u5229\u7528\u6700\u5c0f\u5272(mincut)\u7684\u8fed\u4ee3\u7b97\u6cd5\u89e3\u51b3\u8d85\u56fe\u4e8c\u5206\u95ee\u9898\u3002\u8be5\u7b97\u6cd5\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u662f\u7ebf\u6027\u7684\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u7edd\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u8be5\u7b97\u6cd5\u90fd\u53ea\u9700\u8981\u5f88\u5c11\u6b21\u6570\u7684\u8fed\u4ee3\u3002\u7b97\u6cd5\u6709\u4e09\u4e2a\u7279\u70b9\uff1a 1. \u8d85\u56fe\u88ab\u5206\u6210\u4e24\u4e2aBlock\u3002\u6bcf\u6b21\u79fb\u52a8\u4e00\u4e2a\u7ed3\u70b9\u628a\u5b83\u4ece\u539f\u6765\u7684Block\u79fb\u5f80\u53e6\u4e00\u4e2aBlock\u3002\u540c\u65f6\u7ef4\u6301\u4e24\u4e2aBlock\u7684\u5e73\u8861\u3002\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u4e2a\u5e73\u8861\u4e0d\u662f\u57fa\u4e8e\u6bcf\u4e2aBlock\u4e2d\u7684\u7ed3\u70b9\u6570\u91cf\uff0c\u800c\u662f\u66f4\u4e00\u822c\u7684size of block\u7684\u6982\u5ff5\uff0c\u5b83\u8003\u8651\u5230\u4e86\u6bcf\u4e2a\u7ed3\u70b9\u7684\u6743\u91cd\u662f\u4e0d\u4e00\u6837\u7684\u3002 2. \u5229\u7528\u4e00\u4e2a\u76f8\u5f53\u9ad8\u6548\u7684\u6570\u636e\u7ed3\u6784\uff0c\u53ef\u4ee5\u5728O(1)\u5e38\u6570\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u627e\u5230\u9700\u8981\u79fb\u52a8\u7684\u6700\u4f73\u7ed3\u70b9\u3002 3. \u5728\u79fb\u52a8\u4e86\u67d0\u4e2a\u7ed3\u70b9\u540e\uff0c\u518d\u9ad8\u6548\u5730\u66f4\u65b0\u53d7\u4e0a\u6b21\u79fb\u52a8\u5f71\u54cd\u7684\u7ed3\u70b9\u7684\u4fe1\u606f(\u5373\u8bba\u6587\u540e\u9762\u4f1a\u63d0\u5230\u7684\u7ed3\u70b9\u7684gain\u503c)\u3002\u8fd9\u7b2c\u4e09\u4e2a\u7279\u70b9\u4ea6\u5728\u8bba\u6587\u7684Introduction\u4e2d\u88ab\u518d\u6b21\u63d0\u5230\uff0c\u4f5c\u8005\u8ba4\u4e3a\u8fd9\u662f\u8be5\u8bba\u6587\u7684\u4e3b\u8981\u8d21\u732e(main contribution). \u672f\u8bed\u53ca\u57fa\u672c\u6982\u5ff5 n(i): \u5f53i\u662f\u8d85\u8fb9\u7684\u7f16\u53f7\u65f6\uff0cn(i)\u5b9a\u4e49\u4e3a\u6bcf\u4e2a\u8d85\u8fb9\u4e0a\u7684\u7ed3\u70b9\u6570\u76ee\u3002 s(i)\u6216p(i): \u5f53i\u8868\u793a\u7ed3\u70b9\u65f6\uff0cs(i)\u6216p(i)\u8868\u793a\u7ed3\u70b9\u4e0a\u7684PIN\u6570\u76ee\uff0c\u5373\u7ed3\u70b9\u4e00\u5171\u8ddf\u591a\u4e2a\u6761\u8d85\u8fb9\u6709\u8fde\u63a5\uff0c\u66f4\u591a\u65f6\u5019\u4ea6\u79f0\u4e3a\u7ed3\u70b9\u7684size\u3002 \u90bb\u5c45\u7ed3\u70b9\uff1a \u5982\u679c\u4e24\u4e2a\u7ed3\u70b9\u81f3\u5c11\u80fd\u901a\u8fc7\u4e00\u6761\u8d85\u8fb9\u8fde\u63a5\uff0c\u5373\u4e3a\u90bb\u5c45\u7ed3\u70b9\u3002 A\uff0cB\uff1a \u4ee3\u8868\u8d85\u56fe\u4e8c\u5206\u5272\u540e\u7684\u4e24\u4e2aBLOCK\u3002 \uff5cA\uff5c\uff1a |A| = \\sum_{i=i}^{n}{s(i)} \u5373Block A\u7684size\u5b9a\u4e49\u4e3aBlock A\u4e2d\u6240\u6709\u7684\u7ed3\u70b9\u7684size\u7684\u8fde\u52a0\u3002 A(n)\u6216B(n)\uff1a n\u8868\u793a\u7f16\u53f7\u4e3an\u7684\u8fb9\uff0cA(n)\u5219\u8868\u793a\u8be5\u6761n\u5728Block A\u4e2d\u7684\u7ed3\u70b9\u6570\u3002 cut: \u5728A\u548cB\u4e2d\u90fd\u6709\u7ed3\u70b9\u7684\u8d85\u8fb9\u3002 cutstate: \u4e00\u6761\u8d85\u8fb9\u662f\u4e0d\u662fcut\uff08\u540e\u6765\u53d1\u5c55\u6210\u591a\u5206\u5272\u95ee\u9898\u4e2d\u7684cutsize\uff09\u3002 cell gains: \u5f53\u79fb\u52a8\u4e00\u4e2a\u7ed3\u70b9\u5230\u53e6\u4e00\u4e2aBLOCK\u65f6\uff0ccut\u51cf\u5c11\u7684\u6570\u76ee\u3002 \u7ef4\u6301\u5e73\u8861 \u6700\u5bb9\u6613\u60f3\u5230\u7684\u662f\u5c31\u662f\u4f7f\u8d85\u56fe\u4e8c\u5206\u5272\u540e\u7684\u4e24\u4e2aBLOCK\u4e2d\u7684\u7ed3\u70b9\u6570\u91cf\u5927\u81f4\u76f8\u540c\u3002\u4e0d\u8fc7\uff0c\u53ef\u4ee5\u7a0d\u5fae\u53d8\u590d\u6742\u4e00\u70b9\uff0c\u5373\u8003\u8651\u6bcf\u4e2a\u7ed3\u70b9\u7684\u6743\u91cd\u3002 * W \uff1d |A| + &hellip; <a href=\"https:\/\/ykyi.net\/?p=1727\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Fiduccia Mattheyses\u7b97\u6cd5(\u5373FM\u7b97\u6cd5)\u7684\u8bba\u6587\u89e3\u8bfb&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[108],"class_list":["post-1727","post","type-post","status-publish","format-standard","hentry","category-tech_articles","tag-108"],"_links":{"self":[{"href":"https:\/\/ykyi.net\/index.php?rest_route=\/wp\/v2\/posts\/1727","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ykyi.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ykyi.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ykyi.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ykyi.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1727"}],"version-history":[{"count":0,"href":"https:\/\/ykyi.net\/index.php?rest_route=\/wp\/v2\/posts\/1727\/revisions"}],"wp:attachment":[{"href":"https:\/\/ykyi.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1727"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ykyi.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1727"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ykyi.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}