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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

ž

log(n) rrlines (MBR) without space control

grid5 (line) without space control rrlines (MBR) with space control grid5 (line) with space control

ŸF l¡Y¢¤£>¥T¦{§l¨L©¤ª«¬š­ ¥P£O®> °¯Y¬²±L¯Y­ ®|³˜­P§´°¯_¡yµ·¶H¸i¹

º{»#¼ ±L¥±L¯Y¬‘® £>¯Y´½ l¾ » £O¯@³_¥i­| l¬#­ ¥P£>®:¥P¿‰±P °¥i¬#±LÀÁE¥i± ¼ ¢š­ ¥´°¥i­>­|­ » ´l °® ®> l¬¤¡ ¼ ¬šÂ›±P´Ã »š»  l¬š¡• l­%¤¯Y¬¤¥_ĚÁ#¢š®:®>Ť¥;Æ# »

­> lš¥, l­:®>Å ¼ ®6¾Ç¯_£>¥,¯_Á˜È ¥i±L®>­ ¼ £>¥­ ® ¯_£O¥i l¬²®>Ś¥,¯@³_¥P£>Æ#¯@Éʬ¤¯˜Â¤¥i­PÄ ¼ ¬šÂŤ¥i¬š±L¥T®>Ś¥PÀËÅ ¼ ³_¥•® ¯ÌÁE¥T­ ¥ ¼ £O±VŤ¥iÂ

 l¬²´l Ã¬¤¥ ¼ £:¯_£O¤¥P£i§Í6­ ¼ £O¥i­>¢š´°®Î®>Ť¥T­>¥ ¼ £O±OÅ®> l¾Ç¥, l­| Ã¬š±L£>¥ ¼ ­ ¥i§

ÏÑÐ Ò Ó8ÔÕÖ:×ØÚÙ4Ö:Û½Ü'ÝFޚßNàÇáOâ>ãâ>Ô6ä'åÊæçÙèÞ{Ó8×ÝÝ

é:ê® £O¥P¥_Ä2éìëHê® £>¥P¥

¼

¬šÂ'¯_®>Ť¥P£íê® £>¥P¥%š¥i­>±L¥i¬šÂ

¼

¬2®>­ŒÉî¥P£>¥|¤¥i­> °¡Y¬š¥i® ¯TÁy¥Î«>ï_ð4¥P¿‰±P °¥i¬2®š¢¤¥Î® ¯;®>Ť¥

¼

±P±L¥i­O­

­ » ¥P¥iÂñš ]òE¥P£>¥i¬š±L¥•Áy¥P®[É¥P¥i¬ñ®>Ť¥'¾ ¼  l¬ñ¾Ç¥i¾Ç¯_£OÀ ¼ ¬šÂ8®>Ť¥Ç­ ¥i±L¯Y¬šÂ ¼ £>À8­ ® ¯_£ ¼ ¡_¥_Ä §ó¥_§ÑÅ ¼ £OÂñš l­ ôy§ º  l¾Ì l´¼ £

š ]òE¥P£>¥i¬š±L¥T¥Lõ˜ l­>®>­|ÁE¥P®Éî¥P¥i¬®>Ś¥'öÎ÷øN± ¼ ±VŤ¥ ¼ ¬šÂ›®>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¬˜ê¾Ç¥i¾Ç¯_£OÀ8 l¬šÂš¥Lõñ­ ® £O¢#±L®>¢¤£>¥_§Ìù|Ś Ã­;­ ¥i±L®> °¯Y¬û l¬2³_¥i­ ®> °¡ ¼ ® ¥i­T®>Ť¥

15

Number of accesses

ž

log(n) rrlines (MBR) without space control

grid5 (line) without space control rrlines (MBR) with space control grid5 (line) with space control

ŸF l¡Y¢¤£>¥T¦{§l¨i¦{ª º ¥ ¼ £O±OűL¯Y­ ®%³˜­P§´°¯_¡Eµ·¶H¸L¹

¼œ»š» ´Ã l± ¼ ®> °¯Y¬Ë¯_ú‡± ¼ ±OŤ¥Lê¯_Á#´Ã °³{ l¯Y¢š­>¬¤¥i­>­|® ¯‰é|öê® £>¥P¥_§

ö ¼ ±VŤ¥Lê¯_Á#´l l³{ °¯Y¢#­ ¼ ´°¡_¯_£O l®>Ś¾Ì­ ¼ ŸH÷é ý_ýÄ{É%Ś Ã±OÅÇ£>¥ ¼ ­>¯Y¬š­

ô˜¬¤¯@É%´l¥i¤¡_¥T¯_úÁQ´°¯{±Oô²­> P¥! ¯_ú®>Ť¥¾Ì¥i¾Ç¯_£>À_Ä

¼

Ÿ‡ °£O­ ®PÄ#É¥,ú·¯Y´l´°¯AÉ ®>Ť¥¤À{¬ ¼ ¾Ì l±; l¬š­>¥P£>®> °¯Y¬ ¼ ´°¡_¯_£O l®>Ś¾ ¯_ú,í&%џ½ö&'('  ­>¢š±VŲ®>Å ¼ ®%®>Ś¥,® £>¥P¥¬š¯{¤¥i­% l¬›é|öê

® £>¥P¥ú¯_£O¾ ®>Ť¥-.0/&123#4(5((6879í&%6ŸFö&'('  Ä ¼ ¬šÂ²®>Ť¥­>¾ ¼ ´l´°¥i­>®|£>¥i±P¢¤£O­O °³_¥,­>¢¤Áš® £O¥P¥T l­:¯_úŤ¥i l¡Yő®

®ÉÄì §ó¥_§  °®±L¯Y¬š­O l­ ®>­¯_ú;®>Ť£>¥P¥8¬š¯{¤¥i­i§ íÀ

¼ Â È ¢#­ ®> l¬¤¡”Á

ù½¯ ®>Ś¥¥Lõ˜® £>¥i¾Ç¥'¯_ú®>Ť¥

»

®> °¯Y¬Ì¯_úH®>Ť¥%¯A³_¥P£>ƚ¯@É ¬š¯{¤¥i­î l¬

®>Ť¥;´°¥ ¼ ³_¥i­Îú£>¯Y¾ ¼ ´l l¬šô_¥i´l Ã­ ®¯_úH Ã¬šÂ¤¥Lõ ¼ Á#´°¥%¯_Á¤È¥i±L®>­Î® ¯ ¼ ´l l¬¤ô_¥i´l l­ ®¯_ú968.?|¯_úH¯_Á˜È ¥i±L®>­PĤÉ%Ś¥P£>¥%¥ ¼ ±VÅ

±OÅ{¢š¬¤ôË l­ ¼ ´Ã´°¯{± ¼ ® ¥i l¬²±L¯Y¬‘®> l¡Y¢¤¯Y¢š­%¾Ì¥i¾Ç¯_£>À ¼ ­ ¼ ¬ ¼ £>£ ¼ À_§A@ ¼ ±OÅ´l¥ ¼ ú‡¬š¯{¤¥Ñ¯_ú‡®>Ť¥,é|öê® £>¥P¥•¾ ¼  l¬2® ¼  l¬š­

¼Ç» ¯Y l¬2®Î® ¯Ì®>Ť¥,ÁE¥P¡Y l¬š¬# l¬¤¡T¯_ú ¼ ±VÅ2¢#¬¤ô‘ꍴàl­ ®P§

)”¥ É% l´l´ú¯˜±P¢š­,¯Y¬®>Ť¥ ­ ¥ ¼ £O±OÅ » ¥P£>ú·¯_£O¾ ¼ ¬š±L¥‰¯_ú|± ¼ ±OŤ¥Lê¯_Á#´Ã °³{ l¯Y¢š­Té|öê® £>¥P¥_§8«¬ü¯Y¢¤£T¥Lõ » ¥P£O l¾Ç¥i¬2®>­PÄ

É±L¯Y¾ »#¼ £>¥i“®>Ś¥›­ ¥ ¼ £O±OÅè®> l¾Ç¥²ÁE¥P®Éî¥P¥i¬“®>Ť¥›± ¼ ±VŤ¥Lê¯_Á#´l °³˜ °¯Y¢š­Çé|öê® £O¥P¥ ¼ ¬šÂt®>Ť¥›é|öê® £>¥P¥É% °®>Ť¯Y¢¤®

­>¢š±VÅ ¼ £>£ ¼ ¬¤¡_¥i¾Ç¥i¬2®>­P§4ù%Ť¥CB6« º  ¼ ® ¼ ­ ¥P®>­ ¼ £>¥ñ¢š­ ¥i“ú·¯_£‰®>Ś Ã­ » ¢¤£ » ¯Y­ ¥_§D% ¼ ® ¼ Ä| Ã¬š±P´l¢šÂš Ã¬¤¡8£O¥i±L® ¼ ¬¤¡Y´°¥

š¥i  l¬2® ¯t®>Ť¥ ¾Ç¥i¾Ç¯_£>ÀèÁE¥Pú·¯_£>¥  l¬š­ ¥P£>®> l¯Y¬

¼

¬šÂ­ ¥

¼

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