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u%$U Ã Y ÃX ý=ý=ý Ã 0 Êxa& ! ÿ10 a! 0 aX&=r
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!
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60 80 100 120 140 160 180 200 220 240 260
11.5 12 12.5 13 13.5 14 14.5 15 15.5
Number of accesses
log(n) rrlines (MBR) without space control
grid5 (line) without space control rrlines (MBR) with space control grid5 (line) with space control
F l¡Y¢¤£>¥T¦{§l¨L©¤ª«¬¥P£O®> °¯Y¬²±L¯Y®|³P§´°¯_¡yµ·¶H¸i¹
º{»#¼ ±L¥±L¯Y¬®£>¯Y´½ l¾ » £O¯@³_¥i| l¬#¥P£>®:¥P¿±P °¥i¬#±LÀÁE¥i± ¼ ¢¥´°¥i>| » ´l °®®> l¬¤¡ ¼ ¬Â±P´Ã »» l¬¡ l%¤¯Y¬¤¥_ÄÁ#¢®:®>Ť¥;Æ# »
> lÂ¥, l:®>Å ¼ ®6¾Ç¯_£>¥,¯_ÁÈ¥i±L®> ¼ £>¥®¯_£O¥i l¬²®>Å¥,¯@³_¥P£>Æ#¯@Éʬ¤¯Â¤¥iPÄ ¼ ¬ÂŤ¥i¬±L¥T®>Å¥PÀËÅ ¼ ³_¥®¯ÌÁE¥T¥ ¼ £O±VŤ¥iÂ
l¬²´l 줥 ¼ £:¯_£O¤¥P£i§Í6 ¼ £O¥i>¢´°®Î®>Ť¥T>¥ ¼ £O±OÅ®> l¾Ç¥, l| ì±L£>¥ ¼ ¥i§
ÏÑÐÒ Ó8ÔÕÖ:×ØÚÙ4Ö:Û½Ü'ÝFÞßNàÇáOâ>ãâ>Ô6ä'åÊæçÙèÞ{Ó8×ÝÝ
é:ꮣO¥P¥_Ä2éìëHꮣ>¥P¥
¼
¬Â'¯_®>Ť¥P£íꮣ>¥P¥%Â¥i>±L¥i¬Â
¼
¬2®>Éî¥P£>¥|¤¥i> °¡Y¬¥i®¯TÁy¥Î«>ï_ð4¥P¿±P °¥i¬2®Â¢¤¥Î®¯;®>Ť¥
¼
±P±L¥iO
» ¥P¥iÂñ ]òE¥P£>¥i¬±L¥Áy¥P®[É¥P¥i¬ñ®>Ť¥'¾ ¼ l¬ñ¾Ç¥i¾Ç¯_£OÀ ¼ ¬Â8®>Ť¥Ç¥i±L¯Y¬Â ¼ £>À8®¯_£ ¼ ¡_¥_Ä §ó¥_§ÑÅ ¼ £OÂñ lôy§ º l¾Ì l´¼ £
 ]òE¥P£>¥i¬±L¥T¥Lõ l>®>|ÁE¥P®Éî¥P¥i¬®>Å¥'öÎ÷øN± ¼ ±VŤ¥ ¼ ¬Â®>Ť¥¾ ¼ l¬¾Ì¥i¾Ç¯_£>À_§|ù|Ť¥P£O¥Pú¯_£>¥_Ä#®>Ť¥ lO>¢¤¥i:¯_ú± ¼ ±VŤ¥
¥LòE¥i±L®>¬¤¥P¥iÂû®¯ÁE¥'±L¯Y¬#> l¤¥P£>¥iÂûú¯_£ ¼ ¬ü l¬ê¾Ç¥i¾Ç¯_£OÀ8 l¬Â¥Lõñ®£O¢#±L®>¢¤£>¥_§Ìù|Å Ã;¥i±L®> °¯Y¬û l¬2³_¥i®> °¡ ¼ ®¥iT®>Ť¥
15
Number of accesses
log(n) rrlines (MBR) without space control
grid5 (line) without space control rrlines (MBR) with space control grid5 (line) with space control
F l¡Y¢¤£>¥T¦{§l¨i¦{ª º ¥ ¼ £O±OűL¯Y®%³P§´°¯_¡Eµ·¶H¸L¹
¼»» ´Ã l± ¼ ®> °¯Y¬Ë¯_ú± ¼ ±OŤ¥Lê¯_Á#´Ã °³{ l¯Y¢>¬¤¥i>|®¯é|öꮣ>¥P¥_§
ö ¼ ±VŤ¥Lê¯_Á#´l l³{ °¯Y¢# ¼ ´°¡_¯_£O l®>Å¾Ì ¼ H÷é ý_ýÄ{É%ŠñOÅÇ£>¥ ¼ >¯Y¬
ô¬¤¯@É%´l¥i¤¡_¥T¯_úÁQ´°¯{±Oô²> P¥! ¯_ú®>Ť¥¾Ì¥i¾Ç¯_£>À_Ä
¼
°£O®PÄ#É¥,ú·¯Y´l´°¯AÉ ®>Ť¥Â¤À{¬ ¼ ¾Ì l±; l¬>¥P£>®> °¯Y¬ ¼ ´°¡_¯_£O l®>ž ¯_ú,í&%ѽö&'(' >¢±VŲ®>Å ¼ ®%®>Å¥,®£>¥P¥¬¯{¤¥i% l¬é|öê
®£>¥P¥ú¯_£O¾ ®>Ť¥-.0/&123#4(5((6879í&%6Fö&'(' Ä ¼ ¬Â²®>Ť¥>¾ ¼ ´l´°¥i>®|£>¥i±P¢¤£OO °³_¥,>¢¤Á®£O¥P¥T l:¯_úŤ¥i l¡YÅ®
®ÉÄì §ó¥_§ °®±L¯Y¬O l®>¯_ú;®>Ť£>¥P¥8¬¯{¤¥ii§ íÀ
¼  Ȣ#®> l¬¤¡Á
ù½¯ ®>Å¥¥Lõ®£>¥i¾Ç¥'¯_ú®>Ť¥
»
®> °¯Y¬Ì¯_úH®>Ť¥%¯A³_¥P£>Ư@É ¬¯{¤¥iî l¬
®>Ť¥;´°¥ ¼ ³_¥iÎú£>¯Y¾ ¼ ´l l¬ô_¥i´l î¯_úH 줥Lõ ¼ Á#´°¥%¯_Á¤È¥i±L®>ή¯ ¼ ´l l¬¤ô_¥i´l l®¯_ú968.?|¯_úH¯_ÁÈ¥i±L®>PĤÉ%Å¥P£>¥%¥ ¼ ±VÅ
±OÅ{¢¬¤ôË l ¼ ´Ã´°¯{± ¼ ®¥i l¬²±L¯Y¬®> l¡Y¢¤¯Y¢%¾Ì¥i¾Ç¯_£>À ¼ ¼ ¬ ¼ £>£ ¼ À_§A@ ¼ ±OÅ´l¥ ¼ ú¬¯{¤¥Ñ¯_ú®>Ť¥,é|öꮣ>¥P¥¾ ¼ l¬2® ¼ l¬
¼Ç» ¯Y l¬2®Î®¯Ì®>Ť¥,ÁE¥P¡Y l¬¬# l¬¤¡T¯_ú ¼ ±VÅ2¢#¬¤ôê´Ã l®P§
)¥ É% l´l´ú¯±P¢,¯Y¬®>Ť¥ ¥ ¼ £O±OÅ » ¥P£>ú·¯_£O¾ ¼ ¬±L¥¯_ú|± ¼ ±OŤ¥Lê¯_Á#´Ã °³{ l¯Y¢Té|öꮣ>¥P¥_§8«¬ü¯Y¢¤£T¥Lõ » ¥P£O l¾Ç¥i¬2®>PÄ
ÉL¯Y¾ »#¼ £>¥i®>Å¥¥ ¼ £O±OÅè®> l¾Ç¥²ÁE¥P®Éî¥P¥i¬®>Ť¥± ¼ ±VŤ¥Lê¯_Á#´l °³ °¯Y¢Çé|öꮣO¥P¥ ¼ ¬Ât®>Ť¥é|öꮣ>¥P¥É% °®>Ť¯Y¢¤®
>¢±VÅ ¼ £>£ ¼ ¬¤¡_¥i¾Ç¥i¬2®>P§4ù%Ť¥CB6« º  ¼ ® ¼ ¥P®> ¼ £>¥ñ¢¥iÂú·¯_£®>Å Ã » ¢¤£ » ¯Y¥_§D% ¼ ® ¼ Ä| ì±P´l¢Â 줡8£O¥i±L® ¼ ¬¤¡Y´°¥
Â¥i l¬2®¯t®>Ť¥ ¾Ç¥i¾Ç¯_£>ÀèÁE¥Pú·¯_£>¥ l¬¥P£>®> l¯Y¬
¼
¬Â¥
¼
£O±VÅ
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