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Algorithm Database
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Ræœ¨ - Wikipedia
2æ¬¡å…ƒçŸ©å½¢ã®Ræœ¨ã®ä¾‹ Ræœ¨ï¼ˆè‹±: R-treeï¼‰ã¯ã€Bæœ¨ã«ä¼¼ãŸæœ¨æ§‹é€ ã®ãƒ‡ãƒ¼ã‚¿æ§‹é€ ã§ã‚ã‚Šã€å¤šæ¬¡å…ƒæƒ…å ±ï¼ˆä¾‹ãˆã°ã€äºŒæ¬¡å…ƒåº§æ¨™ãƒ‡ãƒ¼ã‚¿ãªã©ï¼‰ã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ä»˜ã‘ã€ã™ãªã‚ã¡ç©ºé–“ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ã«ä½¿ã‚ã‚Œã‚‹ã€‚ãã‚Œã¯ä¾‹ãˆã°ã€ã€Œç¾åœ¨ä½ç½®ã‹ã‚‰2kmä»¥å†…ã®å…¨ã¦ã®ç¾Žè¡“é¤¨ã‚’æŽ¢ã™ã€ã¨ã„ã£ãŸç”¨é€”ã«ä½¿ã‚ã‚Œã‚‹ã€‚ Ræœ¨ã¯ã€éšŽå±¤çš„ã«å…¥ã‚Œåã«ãªã£ãŸç›¸äº’ã«é‡ãªã‚Šåˆã†æœ€å°å¤–æŽ¥çŸ©å½¢ (MBR) ã§ç©ºé–“ã‚’åˆ†å‰²ã™ã‚‹ã€‚Ræœ¨ã®Rã¯çŸ©å½¢ (Rectangle) ã‚’æ„å‘³ã™ã‚‹ã€‚ Ræœ¨ã®å„ãƒŽãƒ¼ãƒ‰ã®ã‚¨ãƒ³ãƒˆãƒªæ•°ã¯å¯å¤‰ã§ã‚ã‚‹ï¼ˆäº‹å‰ã«å®šç¾©ã•ã‚ŒãŸä¸Šé™ãŒã‚ã‚‹ï¼‰ã€‚è‘‰ãƒŽãƒ¼ãƒ‰ä»¥å¤–ã®å„ã‚¨ãƒ³ãƒˆãƒªã«ã¯2ã¤ã®ãƒ‡ãƒ¼ã‚¿ãŒæ ¼ç´ã•ã‚Œã‚‹ã€‚1ã¤ã¯åãƒŽãƒ¼ãƒ‰ã¸ã®å‚ç…§ã§ã‚ã‚Šã€ã‚‚ã†1ã¤ã¯ãã®åãƒŽãƒ¼ãƒ‰ã®å…¨ã‚¨ãƒ³ãƒˆãƒªã‚’å›²ã‚€å¤–æŽ¥çŸ©å½¢ã®ãƒ‡ãƒ¼ã‚¿ã§ã‚ã‚‹ã€‚ æŒ¿å…¥ãŠã‚ˆã³å‰Šé™¤ã®ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã¯ã“ã‚Œã‚‰ã®å¤–æŽ¥çŸ©å½¢ã‚’ä½¿ã„ã€è¿‘ã„è¦ç´ ãŒåŒã˜è‘‰ãƒŽãƒ¼ãƒ‰ã«å±žã™ã‚‹ã‚ˆã†ã«ã™ã‚‹ï¼ˆç‰¹ã«ã€æ–°ãŸãªè¦ç´ ã‚’æŒ¿å…¥ã™ã‚‹éš›ã«ã€ã©ã®æœ€ä¸‹å±¤ã®å¤–æŽ¥çŸ©å½¢ã«ã‚‚åŽã¾ã‚‰ãªã„å ´
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kdæœ¨ - Wikipedia
3æ¬¡å…ƒã®kdæœ¨ã€‚æ ¹ã‚»ãƒ«ï¼ˆç™½ï¼‰ã‚’ã¾ãš2ã¤ã®éƒ¨åˆ†ã‚»ãƒ«ã«åˆ†å‰²ï¼ˆèµ¤ï¼‰ã—ã€ãã‚Œãžã‚Œã‚’ã•ã‚‰ã«2ã¤ã«åˆ†å‰²ï¼ˆç·‘ï¼‰ã—ã¦ã„ã‚‹ã€‚æœ€å¾Œã«4ã¤ã®ã‚»ãƒ«ãã‚Œãžã‚Œã‚’2ã¤ã«åˆ†å‰²ï¼ˆé’ï¼‰ã—ã¦ã„ã‚‹ã€‚ãã‚Œä»¥ä¸Šã®åˆ†å‰²ã¯ã•ã‚Œã¦ã„ãªã„ã®ã§ã€æœ€çµ‚çš„ã«ã§ããŸ8ã¤ã®ã‚»ãƒ«ã‚’è‘‰ã‚»ãƒ«ã¨å‘¼ã¶ã€‚é»„è‰²ã®çƒã¯æœ¨ã®é ‚ç‚¹ã‚’è¡¨ã—ã¦ã„ã‚‹ã€‚ kdæœ¨ï¼ˆè‹±: kd-tree, k-dimensional treeï¼‰ã¯ã€kæ¬¡å…ƒã®ãƒ¦ãƒ¼ã‚¯ãƒªãƒƒãƒ‰ç©ºé–“ã«ã‚ã‚‹ç‚¹ã‚’åˆ†é¡žã™ã‚‹ç©ºé–“åˆ†å‰²ãƒ‡ãƒ¼ã‚¿æ§‹é€ ã§ã‚ã‚‹ã€‚kdæœ¨ã¯ã€å¤šæ¬¡å…ƒæŽ¢ç´¢éµã‚’ä½¿ã£ãŸæŽ¢ç´¢ï¼ˆä¾‹ãˆã°ã€ç¯„å›²æŽ¢ç´¢ã‚„æœ€è¿‘å‚æŽ¢ç´¢ï¼‰ãªã©ã®ç”¨é€”ã«ä½¿ã‚ã‚Œã‚‹ãƒ‡ãƒ¼ã‚¿æ§‹é€ ã§ã‚ã‚‹ã€‚kdæœ¨ã¯BSPæœ¨ã®ç‰¹æ®Šã‚±ãƒ¼ã‚¹ã§ã‚ã‚‹ã€‚ kdæœ¨ã¯ã€åº§æ¨™è»¸ã®1ã¤ã«åž‚ç›´ãªå¹³é¢ã ã‘ã‚’ä½¿ã£ã¦åˆ†å‰²ã‚’è¡Œã†ã€‚BSPæœ¨ã§ã¯åˆ†å‰²å¹³é¢ã®è§’åº¦ã¯ä»»æ„ã§ã‚ã‚‹ã€‚ã•ã‚‰ã«ä¸€èˆ¬çš„ã«ã¯ã€kdæœ¨ã®æ ¹ãƒŽãƒ¼ãƒ‰ã‹ã‚‰è‘‰ãƒŽãƒ¼ãƒ‰ã¾ã§ã®å„ãƒŽãƒ¼ãƒ‰ã«ã¯1ã¤ã®ç‚¹ãŒæ ¼ç´ã•ã‚Œã‚‹[1]ã€‚ã“ã®ç‚¹ã‚‚BSPæœ¨ã¨ã¯ç•°ãªã‚Šã€BSPæœ¨ã§ã¯è‘‰ãƒŽãƒ¼ãƒ‰ã®ã¿ãŒç‚¹ï¼ˆã¾
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æœ€è¿‘å‚æŽ¢ç´¢ï¼ˆè‹±: Nearest neighbor search, NNSï¼‰ã¯ã€è·é›¢ç©ºé–“ã«ãŠã‘ã‚‹æœ€ã‚‚è¿‘ã„ç‚¹ã‚’æŽ¢ã™æœ€é©åŒ–å•é¡Œã®ä¸€ç¨®ã€ã‚ã‚‹ã„ã¯ãã®è§£æ³•ã€‚è¿‘æŽ¥æŽ¢ç´¢ï¼ˆè‹±: proximity searchï¼‰ã€é¡žä¼¼æŽ¢ç´¢ï¼ˆè‹±: similarity searchï¼‰ã€æœ€è¿‘ç‚¹æŽ¢ç´¢ï¼ˆè‹±: closest point searchï¼‰ãªã©ã¨ã‚‚å‘¼ã¶ã€‚å•é¡Œã¯ã™ãªã‚ã¡ã€è·é›¢ç©ºé–“ M ã«ãŠã‘ã‚‹ç‚¹ã®é›†åˆ S ãŒã‚ã‚Šã€ã‚¯ã‚¨ãƒªç‚¹ q âˆˆ M ãŒã‚ã‚‹ã¨ãã€S ã®ä¸ã§ q ã«æœ€ã‚‚è¿‘ã„ç‚¹ã‚’æŽ¢ã™ã€ã¨ã„ã†å•é¡Œã§ã‚ã‚‹ã€‚å¤šãã®å ´åˆã€M ã«ã¯ dæ¬¡å…ƒã®ãƒ¦ãƒ¼ã‚¯ãƒªãƒƒãƒ‰ç©ºé–“ãŒæŽ¡ç”¨ã•ã‚Œã€è·é›¢ã¯ãƒ¦ãƒ¼ã‚¯ãƒªãƒƒãƒ‰è·é›¢ã‹ãƒžãƒ³ãƒãƒƒã‚¿ãƒ³è·é›¢ã§æ¸¬å®šã•ã‚Œã‚‹ã€‚ä½Žæ¬¡å…ƒã®å ´åˆã¨é«˜æ¬¡å…ƒã®å ´åˆã§ç•°ãªã‚‹ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ãŒã¨ã‚‰ã‚Œã‚‹ã€‚ ãƒ‰ãƒŠãƒ«ãƒ‰ãƒ»ã‚¯ãƒŒãƒ¼ã‚¹ã¯ã€The Art of Computer Programming Vol.3ï¼ˆ1973å¹´ï¼‰ã§ã€ã“ã‚Œã‚’éƒµä¾¿å±€ã®å•é¡Œã§è¡¨ã—ãŸã€‚ã“ã‚Œã¯ã™ãª
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