{"id":104,"date":"2026-06-02T14:21:34","date_gmt":"2026-06-02T06:21:34","guid":{"rendered":"http:\/\/121.199.163.110\/?p=104"},"modified":"2026-06-02T14:41:43","modified_gmt":"2026-06-02T06:41:43","slug":"%e5%ad%a6%e4%b9%a0%e5%9e%8b%e7%b4%a2%e5%bc%95sprig%ef%bc%88sprig%e5%8f%98%e4%bd%93%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.restia.site\/index.php\/2026\/06\/02\/%e5%ad%a6%e4%b9%a0%e5%9e%8b%e7%b4%a2%e5%bc%95sprig%ef%bc%88sprig%e5%8f%98%e4%bd%93%ef%bc%89\/","title":{"rendered":"\u5b66\u4e60\u578b\u7d22\u5f15SPRIG+\uff08SPRIG\u53d8\u4f53\uff09"},"content":{"rendered":"\n

\u8bba\u6587\uff1aEfficient Learned Spatial Index With Interpolation Function Based Learned Model<\/strong><\/p>\n\n\n\n

IEE \u94fe\u63a5\uff1ahttps:\/\/ieeexplore.ieee.org\/abstract\/document\/9816118<\/a><\/p>\n\n\n\n

<\/p>\n\n\n\n

SPRIG\u4e4b\u524d\u7684\u5904\u7406\u65b9\u6cd5\uff1a<\/strong><\/p>\n\n\n\n

\u7d22\u5f15\u6784\u5efa\uff1a<\/strong> SPRIG \u7cfb\u7edf\u5305\u62ec\u4e09\u4e2a\u7ec4\u4ef6\uff1a1\uff09n \u00d7 m \u7f51\u683c\u5e03\u5c40 Gn\u00d7m\uff0c\u5176\u4e2d n \u662f\u6cbf x \u7ef4\u5ea6\u7684\u5217\u6570\uff0cm \u662f\u6cbf y \u7ef4\u5ea6\u7684\u884c\u6570\uff1b2\uff09\u4e00\u4e2a\u8868 T\uff1b3\uff09\u57fa\u4e8e\u7a7a\u95f4\u63d2\u503c\u51fd\u6570\u7684\u5b66\u4e60\u6a21\u578b M\u3002<\/p>\n\n\n\n

\u6784\u5efa Gn\u00d7m \u7684\u4e3b\u8981\u601d\u60f3\u662f\u627e\u5230\u6bcf\u4e2a\u7ef4\u5ea6\u7684\u8fb9\u754c\u503c\u3002\u8fd9\u4e9b\u8fb9\u754c\u503c\u53ef\u4ee5\u5c06\u7a7a\u95f4\u5212\u5206\u4e3a\u6cbf\u4e00\u4e2a\u7ef4\u5ea6\u7684\u591a\u4e2a\u5217\uff0c\u5e76\u786e\u4fdd\u6bcf\u4e2a\u5217\u5177\u6709\u51e0\u4e4e\u76f8\u7b49\u7684\u6570\u636e\u8bb0\u5f55\u6570\u3002\u5b9a\u4e49 x \u548c y \u7ef4\u5ea6\u7684\u8fb9\u754c\u4e3a\u96c6\u5408 Bx \u548c By\uff0c\u5176\u4e2d |Bx| = n + 1\uff0c|By| = m + 1\u3002\u603b\u5171\u6709 n \u00d7 m \u4e2a\u7f51\u683c\u5355\u5143\uff0c\u6211\u4eec\u6709 Gn\u00d7m = {Bx, By}\u3002<\/p>\n\n\n\n

\u63a5\u4e0b\u6765\uff0c\u91c7\u7528\u7b80\u5355\u7684\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u5bf9\u8fd9\u4e9b\u5355\u5143\u8fdb\u884c\u7d22\u5f15\u3002\u9996\u5148\uff0c\u5c06\u6574\u6570\u5206\u914d\u5728\u8303\u56f4 [0, n \u00d7 m – 1] \u5185\u4f5c\u4e3a\u6cbf x \u7ef4\u5ea6\u7684\u5355\u5143 ID\uff0c\u5e76\u5b9a\u4e49\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4 Cid \u6765\u5b58\u50a8\u8fd9\u4e9b\u5355\u5143 ID\uff1aCid[i][j] = j + n * i\uff0c\u5176\u4e2d 0 \u2264 i < n \u4e14 0 \u2264 j < m\u3002\u7136\u540e\uff0c\u53ef\u4ee5\u5efa\u7acb\u4e00\u4e2a\u8868 T \u5c06\u5355\u5143 ID \u6620\u5c04\u5230\u8986\u76d6\u8bb0\u5f55\uff0c\u5176\u4e2d\u952e\u662f\u5355\u5143 ID\uff0c\u503c\u662f\u4e00\u4e2a\u8868\u793a\u6307\u5411\u7b2c\u4e00\u6761\u8bb0\u5f55\u7684\u6307\u9488\u548c\u5355\u5143\u4e2d\u8bb0\u5f55\u6570\u7684\u5bf9\uff08firstAddress, size\uff09\u3002\u57fa\u4e8e Gn\u00d7m \u548c Cid\uff0c\u6211\u4eec\u53ef\u4ee5\u62df\u5408\u7a7a\u95f4\u63d2\u503c\u51fd\u6570 Cid * M(Bx, By) \u4f5c\u4e3a\u6211\u4eec\u7684\u5b66\u4e60\u6a21\u578b\u3002<\/p>\n\n\n\n

\u67e5\u8be2\u5904\u7406\uff1a<\/strong> \u5904\u7406\u67e5\u8be2\u7684\u539f\u5219\u662f\u5b9a\u4f4d\u5305\u542b\u67e5\u8be2\u70b9\u7684\u5355\u5143\u3002\u7136\u540e\uff0c\u57fa\u4e8e\u5b9a\u4f4d\u5230\u7684\u5355\u5143\uff0c\u53ef\u4ee5\u91c7\u7528\u8303\u56f4\u67e5\u8be2\u548c kNN \u67e5\u8be2\u7b56\u7565\u6765\u8fc7\u6ee4\u548c\u7ec6\u5316\u6240\u9700\u7684\u6570\u636e\u70b9\u3002\u5177\u4f53\u800c\u8a00\uff0c\u5b9a\u4f4d\u8986\u76d6\u67e5\u8be2\u70b9\u7684\u5355\u5143\u6709\u4e24\u4e2a\u6b65\u9aa4\uff1a<\/p>\n\n\n\n

Step-1: \u9884\u6d4b\u5355\u5143 ID\uff08cell id\uff09<\/strong> \u7ed9\u5b9a\u67e5\u8be2\u70b9 (xq, yq)\uff0c\u53ef\u4ee5\u4f7f\u7528\u5b66\u4e60\u6a21\u578b\u83b7\u5f97\u9884\u6d4b\u7684\u5355\u5143 ID\uff0c\u5373 pid = M(xq, yq)\u3002\u7136\u540e\uff0c\u53ef\u4ee5\u7b80\u5355\u5730\u8ba1\u7b97 pid \u5728 Bx \u548c By \u96c6\u5408\u4e2d\u7684\u4f4d\u7f6e\u3002\u4e5f\u5c31\u662f\u8bf4\uff0clpx = pid mod n\uff0clpy = pid \/\/ n\u3002<\/p>\n\n\n\n

Step-2: \u7528\u672c\u5730\u4e8c\u8fdb\u5236\u641c\u7d22\u5b9a\u4f4d\u5b9e\u9645\u5355\u5143 ID<\/strong> \u7ed9\u5b9a\u9519\u8bef\u4fdd\u8bc1\u7684\u4e00\u5bf9\u503c (egx, egy)\uff0c\u901a\u8fc7\u5728 Bx \u548c By \u4e0a\u8fdb\u884c\u672c\u5730\u4e8c\u8fdb\u5236\u641c\u7d22\uff0c\u53ef\u4ee5\u83b7\u5f97\u67e5\u8be2\u70b9\u7684\u5b9e\u9645 x \u548c y \u4f4d\u7f6e\uff0c\u5206\u522b\u8868\u793a\u4e3a lrx \u548c lry\u3002\u5728 Bx \u96c6\u5408\u4e0a\u7684\u641c\u7d22\u8303\u56f4\u662f [lpx – egx, lpx + egx]\uff0c\u800c\u5728 By \u96c6\u5408\u4e0a\u662f [lpy – egy, lpy + egy]\u3002\u6700\u540e\uff0c\u53ef\u4ee5\u83b7\u5f97\u67e5\u8be2\u70b9 (xq, yq) \u7684\u5b9e\u9645\u5355\u5143 ID\uff0c\u5373 rid = lry * n + lrx\u3002<\/p>\n\n\n\n

<\/p>\n\n\n\n

\u4ee5 (38, 420) \u4e3a\u4f8b\uff0c\u5b83\u5e94\u8be5\u4f4d\u4e8e\u5355\u5143 ID = 51 \u7684\u5355\u5143\u4e2d\uff0c\u5373 rid = 51\u3002\u5047\u8bbe\u9884\u6d4b\u7684\u5355\u5143 ID pid = M(38, 420) = 44\uff0c\u4e14 (egx, egy) = (1, 2)\u3002\u5728 Step-1 \u4e2d\uff0clpx = pid mod n = 44 mod 8 = 4\uff0clpy = pid \/\/ n = 44 \/\/ 8 = 5\u3002\u5728 Step-2 \u4e2d\uff0c\u7531\u4e8e egx = 1\uff0cBx \u4e0a\u7684\u4e8c\u8fdb\u5236\u641c\u7d22\u8303\u56f4\u662f [3, 5]\uff0c\u800c\u7531\u4e8e egy = 2\uff0cBy \u4e0a\u7684\u641c\u7d22\u8303\u56f4\u662f [3, 7]\u3002\u7531\u4e8e Bx[3] = 31 < 38 < Bx[4] = 42\uff0c\u6211\u4eec\u5f97\u5230 lrx = 3\u3002\u7c7b\u4f3c\u5730\uff0c\u7531\u4e8e By[6] = 410 < 420 < By[7] = 500\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230 lry = 6\u3002\u56e0\u6b64\uff0crid = lry * n + lrx = 6 * 8 + 3 = 51\u3002<\/p>\n\n\n\n

\u83b7\u5f97\u67e5\u8be2\u70b9\u7684\u5b9e\u9645\u5355\u5143 ID rid \u540e\uff0c\u53ef\u4ee5\u4ece\u8be5\u5355\u5143\u5f00\u59cb\u6267\u884c\u8303\u56f4\u67e5\u8be2\u548c kNN \u7b56\u7565\uff0c\u4ee5\u6536\u96c6\u67e5\u8be2\u7ed3\u679c\u3002<\/p>\n\n\n\n

<\/p>\n\n\n\n

SPRIG+<\/strong>\u662f\u5728SPRIG\u7684\u57fa\u7840\u4e0a\u63d0\u51fa\u7684\u591a\u7ef4\u5b66\u4e60\u578b\u7d22\u5f15\u3002SPRIG+\u7684\u6838\u5fc3\u6784\u5efa\u903b\u8f91\u5728\u4e8e\u901a\u8fc7\u6539\u8fdb\u7684IH-tree+<\/strong>\u6a21\u578b\u6765\u6620\u5c04\u4e8c\u7ef4\u7a7a\u95f4\u5750\u6807\u5230\u7f51\u683c\u5355\u5143ID\u3002\u5728\u6784\u9020IH-tree+\u4e4b\u524d\uff0c\u6839\u636e\u6570\u636e\u5206\u5e03\uff0c\u5c06\u4e8c\u7ef4\u7a7a\u95f4\u5212\u5206\u4e3an\u00d7m\u7684\u81ea\u9002\u5e94\u7f51\u683c\uff0c\u751f\u6210x\u548cy\u7ef4\u5ea6\u7684\u8fb9\u754c\u503c\u96c6\u5408Bx\u548cBy\u3002<\/p>\n\n\n\n

IH-tree+\u91c7\u7528\u5e73\u8861\u7684\u56db\u53c9\u6811\u7ed3\u6784\u8fdb\u884c\u6784\u9020\uff0c\u9996\u5148\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u9012\u5f52\u5730\u5c06\u4e8c\u7ef4\u533a\u57df\u5212\u5206\u4e3a\u56db\u4e2a\u5b50\u533a\u57df\u3002\u63a5\u7740\u6bcf\u4e2a\u5185\u90e8\u8282\u70b9\u8bb0\u5f55\u5176\u5bf9\u5e94\u7684\u4e2d\u5fc3\u70b9\u5750\u6807\uff08\u57fa\u4e8eBx\u548cBy\u7684\u7d22\u5f15\u4f4d\u7f6e\uff09\uff0c\u5e76\u6307\u5411\u56db\u4e2a\u5b50\u8282\u70b9\u3002\u5f53\u8fbe\u5230\u9884\u8bbe\u6811\u9ad8h\u65f6\u505c\u6b62\u5212\u5206\u3002IH-tree+\u7684\u53f6\u5b50\u8282\u70b9\u4e0d\u518d\u8fdb\u884c\u590d\u6742\u7684\u51fd\u6570\u62df\u5408\uff0c\u800c\u662f\u76f4\u63a5\u5b58\u50a8\u8be5\u5b50\u533a\u57df\u5728 \u548c \u4e2d\u7684\u8fb9\u754c\u4f4d\u7f6e\u7d22\u5f15\uff08\u56db\u4e2a\u6574\u6570\u503c\uff09\u3002\u5728\u6784\u5efa\u53f6\u5b50\u8282\u70b9\u65f6\uff0c\u5e94\u7528\u52a8\u6001\u7f16\u7801\u6280\u672f\uff0c\u5c06\u5b50\u533a\u57df\u5185\u7684\u5355\u5143ID\u91cd\u65b0\u8fdb\u884c\u5c40\u90e8\u7f16\u7801\uff0c\u4ece\u800c\u786e\u4fdd\u9884\u6d4b\u7ed3\u679c\u88ab\u4e25\u683c\u9650\u5236\u5728\u53f6\u5b50\u8282\u70b9\u8986\u76d6\u7684\u8303\u56f4\u5185\u3002\u5f53\u67e5\u8be2\u70b9\u843d\u5728\u67d0\u4e2a\u53f6\u5b50\u8282\u70b9\u4ee3\u8868\u7684\u5b50\u533a\u57df\u65f6\uff0c\u9996\u5148\u6839\u636e\u8be5\u8282\u70b9\u5b58\u50a8\u7684\u8fb9\u754c\u4f4d\u7f6e\u8ba1\u7b97\u5c40\u90e8\u7f51\u683c\u7684\u89c4\u683c\uff1a<\/p>\n\n\n

\n
\"\"<\/div><\/figure>\n<\/div>\n\n\n

\u7136\u540e\u5728\u5c40\u90e8\u533a\u57df\u5185\uff0c\u56db\u4e2a\u89d2\u70b9\u7684\u5355\u5143\u683c\u4f4d\u7f6e\u503c\u4e0d\u518d\u4f7f\u7528\u5168\u5c40\u7f16\u7801\uff0c\u800c\u662f\u8fdb\u884c\u672c\u5730\u5316\u7f16\u7801\u3002\u56db\u4e2a\u89d2\u70b9\u7684\u503c\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n

\n
\"\"<\/div><\/figure>\n<\/div>\n\n\n

\u63a5\u7740\uff0c\u5229\u7528\u5f52\u4e00\u5316\u540e\u7684\u67e5\u8be2\u5750\u6807\u8ba1\u7b97\u5c40\u90e8\u9884\u6d4b\u4f4d\u7f6e\uff1a<\/p>\n\n\n

\n
\"\"<\/div><\/figure>\n<\/div>\n\n\n

\u6700\u540e\uff0c\u5f97\u5230\u5c40\u90e8\u9884\u6d4bID\u540e\uff0c\u901a\u8fc7\u5750\u6807\u504f\u79fb\u5c06\u5176\u8fd8\u539f\u4e3a\u5168\u5c40\u7f51\u683c\u4e2d\u7684ID\uff1a<\/p>\n\n\n

\n
\"\"<\/div><\/figure>\n<\/div>\n\n\n

\u52a8\u6001\u7f16\u7801\u5f3a\u5236\u9884\u6d4b\u503c\u843d\u5728\u53f6\u5b50\u8282\u70b9\u7684\u8986\u76d6\u8303\u56f4\u5185\uff0c\u63a7\u5236\u8bef\u5dee\u5728\u56fa\u5b9a\u8303\u56f4\u5185\uff0c\u63d0\u9ad8\u4e86\u67e5\u8be2\u7684\u51c6\u786e\u7387\u3002<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

\u8bba\u6587\uff1aEfficient Learned Spatial Index With Interpolation F […]<\/p>\n","protected":false},"author":1,"featured_media":108,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[10,9],"class_list":["post-104","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-learn","tag-10","tag-9"],"_links":{"self":[{"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/posts\/104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/comments?post=104"}],"version-history":[{"count":4,"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/posts\/104\/revisions"}],"predecessor-version":[{"id":116,"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/posts\/104\/revisions\/116"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/media\/108"}],"wp:attachment":[{"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/media?parent=104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/categories?post=104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.restia.site\/index.php\/wp-json\/wp\/v2\/tags?post=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}