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Check root MBR —\noverlaps? Yes →\ndescend\n2. Check MBR_A,\nMBR_B, MBR_C —\nwhich overlap the\ncircle?\n3. Descend only into\noverlapping MBRs\n4. At leaves: exact\ndistance check for\neach business\n\nLike a B-tree:\nbalanced,\ndisk-friendly, O(log N)\nsearch","originalText":"R-Tree Structure\n\nRoot MBR:\n[entire_map]\n\nleaf1 leaf2 leaf3\nleaf4 leaf5 leaf6\n[biz [biz [biz [biz\n[biz [biz\n1-50] 51-90] 91-150]\n... ... ...]\n\nSearch: \"Find all in\ncircle(center, radius)\"\n1. Check root MBR —\noverlaps? Yes →\ndescend\n2. Check MBR_A,\nMBR_B, MBR_C —\nwhich overlap the\ncircle?\n3. Descend only into\noverlapping MBRs\n4. At leaves: exact\ndistance check for\neach business\n\nLike a B-tree:\nbalanced,\ndisk-friendly, O(log N)\nsearch","textAlign":"left","verticalAlign":"middle","containerId":"shape-6","lineHeight":1.3,"autoResize":false,"customData":{"revealStep":4}},{"angle":0,"strokeColor":"#6577aa","backgroundColor":"#eef1fc","fillStyle":"solid","strokeWidth":1.5,"strokeStyle":"solid","roughness":0.7,"opacity":100,"version":1,"versionNonce":1,"isDeleted":false,"groupIds":["step-5"],"frameId":null,"roundness":null,"boundElements":[{"type":"text","id":"shape-9"}],"updated":0,"link":null,"locked":false,"id":"shape-8","type":"rectangle","seed":625,"x":16,"y":1394.2,"width":288,"height":379.2,"customData":{"revealStep":5}},{"angle":0,"strokeColor":"#394557","backgroundColor":"transparent","fillStyle":"solid","strokeWidth":1.5,"strokeStyle":"solid","roughness":0.7,"opacity":100,"version":1,"versionNonce":1,"isDeleted":false,"groupIds":["step-5"],"frameId":null,"roundness":null,"boundElements":null,"updated":0,"link":null,"locked":false,"id":"shape-9","type":"text","seed":698,"x":36,"y":1412.2,"width":248,"height":343.2,"fontSize":22,"fontFamily":1,"text":"How R-Tree Works:\nLike a B-tree, but\nfor spatial data.\nEach node holds a\nbounding box (minimum\nbounding rectangle,\nMBR).\nInternal nodes' MBRs\ncontain all children's\nMBRs.\nLeaves hold actual\ndata points.","originalText":"How R-Tree Works:\nLike a B-tree, but\nfor spatial data.\nEach node holds a\nbounding box (minimum\nbounding rectangle,\nMBR).\nInternal nodes' MBRs\ncontain all children's\nMBRs.\nLeaves hold actual\ndata points.","textAlign":"left","verticalAlign":"middle","containerId":"shape-8","lineHeight":1.3,"autoResize":false,"customData":{"revealStep":5}}],"appState":{"viewBackgroundColor":"#fbfbf8","gridSize":null},"files":{}}