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Fractal Prefetching B·-Trees: Optimizing Both Cache and Disk

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Fractal Prefetching B·-Trees: Optimizing Both Cache and Disk Fractal Prefetching B · -Trees: Optimizing Both Cache and Disk Performance Ü Shimin Chen, Phillip B. Gibbons Ý , Todd C. Mowry, and Gary Valentin Ü School of Computer Science Ý Information Sciences Research Center DB2 UDB Development Team Carnegie Mellon University Bell Laboratories IBM Toronto Lab Pittsburgh, PA 15213 Murray Hill, NJ 07974£ Markham, Ontario, Canada L6G 1C7 g fchensm,tcm @cs.cmu.edu [email protected] ABSTRACT · B ¹ÌÖee× haÚe b eeÒ ØÖadiØiÓÒaÐÐÝ ÓÔØiÑiÞed fÓÖ Á»Ç Ô eÖfÓÖ¹ ÑaÒce ÛiØh di×k Ôage× a× ØÖee ÒÓ de׺ ÊeceÒØÐݸ Öe×eaÖcheÖ× · haÚe ÔÖÓÔ Ó×ed ÒeÛ ØÝÔ e× Óf B ¹ÌÖee× ÓÔØiÑiÞed fÓÖ CÈÍ cache Ô eÖfÓÖÑaÒce iÒ ÑaiÒ ÑeÑÓÖÝ eÒÚiÖÓÒÑeÒØ׸ ÛheÖe Øhe ØÖee ÒÓ de ×iÞe× aÖe ÓÒe ÓÖ a feÛ cache ÐiÒe׺ ÍÒfÓÖØÙÒaØeÐݸ dÙe ÔÖiÑaÖiÐÝ ØÓ Øhi× ÐaÖge di×cÖeÔaÒcÝ iÒ ÓÔØiÑaÐ ÒÓ de ×iÞe׸ · eÜi×ØiÒg di×k¹ÓÔØiÑiÞed B ¹ÌÖee× ×Ù«eÖ fÖÓÑ Ô Ó ÓÖ cache Ô eÖ¹ · fÓÖÑaÒce ÛhiÐe cache¹ÓÔØiÑiÞed B ¹ÌÖee× eÜhibiØ Ô Ó ÓÖ di×k FigÙÖe ½: ËeÐf¹×iÑiÐaÖ \ØÖee ÛiØhiÒ a ØÖee" ×ØÖÙcØÙÖe Ô eÖfÓÖÑaÒceº ÁÒ Øhi× ÔaÔ eÖ¸ Ûe ÔÖÓÔ Ó×e fÖacØaÐ ÔÖefeØch¹ · · iÒg B ¹ÌÖee× ´fÔB ¹ÌÖee×µ¸ ÛhicheÑb ed \cache¹ÓÔØiÑiÞed" ØÖee× ÛiØhiÒ \di×k¹ÓÔØiÑiÞed" ØÖee׸ iÒ ÓÖdeÖ ØÓ ÓÔØiÑiÞe CÈÍ cache Ô eÖfÓÖÑaÒce bÝ ÑiÒiÑiÞiÒg Øhe iÑÔacØ Óf cache · b ÓØh cache aÒd Á»Ç Ô eÖfÓÖÑaÒceº Ïe de×igÒ aÒd eÚaÐÙaØe Ñi××e׺ Ìhe×e \cache¹ÓÔØiÑiÞed" B ¹ÌÖee× aÖe cÓÑÔ Ó×ed Óf ½ ØÛÓ aÔÔÖÓache× ØÓ bÖeakiÒg di×k Ôage× iÒØÓ cache¹ÓÔØiÑiÞed ÒÓ de× Øhe ×iÞe Óf a cache ÐiÒe |iºeº¸ Øhe ÒaØÙÖaÐ ØÖaÒ×feÖ ×iÞe ÒÓ de×: di×k¹¬Ö×Ø aÒd cache¹¬Ö×غ Ìhe×e aÔÔÖÓache× aÖe ×ÓÑe¹ fÓÖ ÖeadiÒg ÓÖ ÛÖiØiÒg ØÓ ÑaiÒ ÑeÑÓÖݺ · ÛhaØ bia×ed iÒ faÚÓÖ Óf ÑaÜiÑiÞiÒg di×k aÒd cache Ô eÖfÓÖ¹ ÍÒfÓÖØÙÒaØeÐݸ B ¹ÌÖee× ÓÔØiÑiÞed fÓÖ di×k ×Ù«eÖ fÖÓÑ · ÑaÒce¸ Öe×Ô ecØiÚeÐݸ a× deÑÓÒ×ØÖaØed bÝ ÓÙÖ Öe×ÙÐØ׺ BÓØh Ô Ó ÓÖ CÈÍ cache Ô eÖfÓÖÑaÒce¸ aÒd B ¹ÌÖee× ÓÔØiÑiÞed fÓÖ · iÑÔÐeÑeÒØaØiÓÒ× Óf fÔB ¹ÌÖee× achieÚe dÖaÑaØicaÐÐÝ b eØØeÖ cache ×Ù«eÖ fÖÓÑ Ô Ó ÓÖ Á»Ç Ô eÖfÓÖÑaÒceº Ìhi× i× ÔÖiÑaÖiÐÝ · cache Ô eÖfÓÖÑaÒce ØhaÒ di×k¹ÓÔØiÑiÞed B ¹ÌÖee×: a facØÓÖ b ecaÙ×e Óf Øhe ÐaÖge di×cÖeÔaÒcÝ iÒ ÒÓ de ×iÞe×: di×k Ôage× aÖe Óf ½º½ß½º8 iÑÔÖÓÚeÑeÒØ fÓÖ ×eaÖch¸ ÙÔ ØÓ a facØÓÖ Óf 4º¾ iѹ ØÝÔicaÐÐÝ 4ÃBß64ÃB ÛhiÐe cache ÐiÒe× aÖe ÓfØeÒ ¿¾Bß½¾8B¸ · ÔÖÓÚeÑeÒØ fÓÖ ÖaÒge ×caÒ׸ aÒd ÙÔ ØÓ a ¾¼¹fÓÐd iÑÔÖÓÚe¹ deÔ eÒdiÒg ÓÒ Øhe ×Ý×ØeѺ ÌhÙ× eÜi×ØiÒg di×k¹ÓÔØiÑiÞed B ¹ ÑeÒØ fÓÖ ÙÔ daØe׸ aÐÐ ÛiØhÓÙØ ×igÒi¬caÒØ degÖadaØiÓÒ Óf Á»Ç ÌÖee× ×Ù«eÖ aÒ eÜce××iÚeÒÙÑb eÖ Óf cache Ñi××e× ØÓ ×eaÖchiÒ · Ô eÖfÓÖÑaÒceº ÁÒ addiØiÓÒ¸ fÔB ¹ÌÖee× acceÐeÖaØe Á»Ç Ô eÖ¹ a ´ÐaÖgeµ ÒÓ de¸ Ûa×ØiÒg ØiÑe aÒd fÓÖciÒg Øhe eÚicØiÓÒ Óf Ù×e¹ fÓÖÑaÒce fÓÖ ÖaÒge ×caÒ× bÝ Ù×iÒg jÙÑÔ¹Ô ÓiÒØeÖ aÖÖaÝ× ØÓ fÙÐ daØa fÖÓÑ Øhe cacheº ÄikeÛi×e¸ eÜi×ØiÒg cache¹ÓÔØiÑiÞed · ÔÖefeØch Ðeaf Ôage׸ ØheÖebÝachieÚiÒg a ×Ô eed¹ÙÔ Óf ¾º5ß5 B ¹ÌÖee׸ iÒ ×eaÖchiÒg fÖÓÑ Øhe ÖÓ ÓØ ØÓ Øhe de×iÖed Ðeaf¸ ÓÒ ÁBÅ³× DB¾ ÍÒiÚeÖ×aÐ DaØaba×eº ÑaÝ feØch a di×ØiÒcØ Ôage fÓÖ each ÒÓ de ÓÒ Øhi× ÔaØhº Ìhi× i× a ×igÒi¬caÒØ Ô eÖfÓÖÑaÒce Ô eÒaÐØݸ fÓÖ Øhe ×ÑaÐÐeÖ ÒÓ de× · he¹ÓÔØiÑiÞed B ¹ÌÖee× iÑÔÐÝ ÑÙch deeÔ eÖ ØÖee× ØhaÒ 1. INTRODUCTION Óf cac · iÒ Øhe di×k¹ÓÔØiÑiÞed ca×e× ´eºgº¸ ØÛice a× deeÔµº Ìhe Á»Ç Ìhe B ¹ÌÖee i× a ÙbiÕÙiØÓÙ× ×ØÖÙcØÙÖe fÓÖ iÒdeÜiÒg di×k¹ Ô eÒaÐØÝ fÓÖ ÖaÒge ×caÒ× ÓÒ ÒÓÒcÐÙ×ØeÖed iÒdeÜe× Óf cache¹ Öe×ideÒØ daØaº ÁØ ÔÖÓÚide× ba×ic iÒdeÜ ÓÔ eÖaØiÓÒ× ×Ùch a× ÓÔØiÑiÞed ØÖee× i× eÚeÒ ÛÓÖ×e: a di×ØiÒcØ Ôage ÑaÝ b e feØched ×eaÖch¸ ÖaÒge ×caÒ¸ iÒ×eÖØiÓÒ aÒd deÐeØiÓÒ¸ ÛhiÐe ÑiÒiÑiÞ¹ fÓÖ each Ðeaf ÒÓ de iÒ Øhe ÖaÒge¸ iÒcÖea×iÒg Øhe ÒÙÑb eÖ Óf di×k iÒg Øhe ÒÙÑbeÖ Óf di×k acce××e׺ ÌÓ ÓÔØiÑiÞe Á»Ç Ô eÖfÓÖ¹ · acce××e× bÝ Øhe ÖaØiÓ Óf Øhe ÒÓ de ×iÞe× ´eºgº¸ a facØÓÖ Óf 5¼¼µº ÑaÒce¸ ØÖadiØiÓÒaÐ \di×k¹ÓÔØiÑiÞed" B ¹ÌÖee× aÖe cÓÑÔ Ó×ed Óf ÒÓ de× Øhe ×iÞe Óf a di×k Ôage|iºeº¸ Øhe ÒaØÙÖaÐ ØÖaÒ×feÖ · ÊeceÒØÐݸ ×eÚeÖaÐ ×ØÙd¹ ×iÞe fÓÖ ÖeadiÒg ÓÖ ÛÖiØiÒg ØÓ di×kº 1.1 Our Approach: Fractal Prefetching B -Trees · ie× [5¸ 6¸ ½9] haÚe cÓÒ×ideÖed B ¹ÌÖee ÚaÖiaÒØ× fÓÖ iÒdeܹ ÁÒ Øhi× ÔaÔ eÖ¸ Ûe ÔÖÓÔ Ó×e aÒd eÚaÐÙaØe FÖacØaÐ ÈÖefeØch¹ · · · iÒg ÑeÑÓÖݹÖe×ideÒØ daØaº Ìhe×e ×ØÙdie× ÔÖe×eÒØ ÒeÛ ØÝÔ e× iÒg B ¹ÌÖee× ´fÔB ¹ÌÖee×µ¸ Ûhich aÖe a ÒeÛ ØÝÔeÓfB ¹ÌÖee · · · Óf B ¹ÌÖee×|cache¹×eÒ×iØiÚe B ¹ÌÖee× [½9]¸ ÔaÖØiaйkeÝ B ¹ ØhaØ ÓÔØiÑiÞe× bÓØh cache aÒd Á»Ç Ô eÖfÓÖÑaÒceº ÁÒ a ÒÙع · · ÌÖee× [5]¸ aÒd ÔÖefeØchiÒg B ¹ÌÖee× [6]|ØhaØ ÓÔØiÑiÞe fÓÖ ×heÐи aÒ fÔB ¹ÌÖee i× a ×iÒgÐe iÒdeÜ ×ØÖÙcØÙÖe ØhaØ caÒ b e ÚieÛed aØ ØÛÓ di«eÖeÒØ gÖaÒÙÐaÖiØie×: aØ a cÓaÖ×e gÖaÒÙÐaÖ¹ £ CÙÖÖeÒØ aÆÐiaØiÓÒ: ÁÒØeÐ Êe×eaÖch ÈiØØ×bÙÖgh¸ 4½7 ËÓÙØh CÖaig Ëغ¸ iØݸ iØ cÓÒØaiÒ× di×k¹ÓÔØiÑiÞed ÒÓ de× ØhaØ aÖe ÖÓÙghÐÝ Øhe ÈiØØ×bÙÖgh¸ ÈA ½5¾½¿ ÔhiÐ ÐiÔºbºgibbÓÒ×@iÒØeкcÓÑ ×iÞe Óf a di×k Ôage¸ aÒd aØ a ¬Òe gÖaÒÙÐaÖiØݸ iØ cÓÒØaiÒ× he¹ÓÔØiÑiÞed ÒÓ de× ØhaØ aÖe ÖÓÙghÐÝ Øhe ×iÞe Óf a cache Permission to make digital or hard copies of all or part of this work for cac · ÐiÒeº Ïe ÖefeÖ ØÓ a fÔB Öee a× b eiÒg \fÖacØaÐ" b ecaÙ×e Óf personal or classroom use is granted without fee provided that copies are ¹Ì not made or distributed for profit or commercial advantage and that copies iØ× ×eÐf¹×iÑiÐaÖ \ØÖee ÛiØhiÒ a ØÖee" ×ØÖÙcØÙÖe¸ a× iÐÐÙ×ØÖaØed FigÙÖe ½º Ìhe cache¹ÓÔØiÑiÞed a×Ô ecØ i× ÑÓ deÐed afØeÖ bear this notice and the full citation on the first page. To copy otherwise, to iÒ · ÔÖefeØchiÒg B ¹ÌÖee× ØhaØ Ûe ÔÖÓÔ Ó×ed eaÖÐieÖ [6]¸ Ûhich republish, to post on servers or to redistribute to lists, requires prior specific Øhe permission and/or a fee. ½ · ÔÖefeØchiÒg B ¹ÌÖee× [6]¸ Øhe ÒÓ de× aÖe ×eÚeÖaÐ cache ACM SIGMOD ’2002 June 4-6, Madison, Wisconsin, USA ÁÒ Øhe ca×e Óf ÐiÒe× Ûideº Copyright 2002 ACM 1-58113-497-5/02/06 ...°5.00. ÛeÖe ×hÓÛÒ ØÓ haÚe Øhe b e×Ø ÑaiÒ ÑeÑÓÖÝ Ô eÖfÓÖÑaÒce fÓÖ ×iÞe ÛheÒ cÓÒ×ideÖiÒg bÙ«eÖ cache Ô eÖfÓÖÑaÒce¸ fÓÖ di×k¹ · ¬Üed¹×iÞe keÝ׺ ´Ïe ÒÓØe¸ hÓÛeÚeÖ¸ ØhaØ Øhi× geÒeÖaÐ aÔ¹ Öe×ideÒØ daØaº ÄÓÑeØ³× ÖeceÒØ ×ÙÖÚeÝ Óf B ¹ÌÖee ØechÒiÕÙe× [½6] · ÔÖÓach caÒ b e aÔÔÐied ØÓ aÒÝ cache¹ÓÔØiÑiÞed B ¹ÌÖeeºµ ÁÒ ÑeÒØiÓÒed Øhe idea Óf iÒØÖa¹ÒÓ de ÑicÖÓ¹iÒdeÜiÒg: iºeº¸ ÔÐac¹ · a ÔÖefeØchiÒg B ¹ÌÖee¸ ÒÓ de× aÖe ×eÚeÖaÐ cache ÐiÒe× Ûide iÒg a ×ÑaÐÐ aÖÖaÝ iÒ a feÛ cache ÐiÒe× Óf Øhe Ôage ØhaØ iÒdeÜe× ´eºgº¸ 8|Øhe eÜacØ ÒÙÑbeÖ i× ØÙÒed accÓÖdiÒg ØÓ ÚaÖiÓÙ× Øhe ÖeÑaiÒiÒg keÝ× iÒ Øhe Ôageº ÏhiÐe iØ aÔÔ eaÖ× ØhaØ Øhi× ÑeÑÓÖÝ ×Ý×ØeÑ ÔaÖaÑeØeÖ×µ¸ aÒd ÔÖefeØchiÒg i× Ù×ed ×Ó ØhaØ idea had ÒÓØ b eeÒ ÔÙÖ×Ùed iÒ aÒÝ deØaiÐ b efÓÖe¸ Ûe cÓÑÔaÖe · Øhe ØiÑe ØÓ feØch a ÒÓ de i× ÒÓØ ÑÙch ÐÓÒgeÖ ØhaÒ Øhe deÐaÝ iØ× Ô eÖfÓÖÑaÒce agaiÒ×Ø fÔB ¹ÌÖee× ÐaØeÖ iÒ ÓÙÖ eÜÔ eÖiÑeÒ¹ fÓÖ a ×iÒgÐe cache Ñi×׺ ØaÐ Öe×ÙÐØ׺ Ïe Ób×eÖÚe ØhaØ ÛhiÐe ÑicÖÓ¹iÒdeÜiÒg achieÚe× · Ïe de×igÒ aÒd eÚaÐÙaØe ØÛÓ aÔÔÖÓache× ØÓ iÑÔÐeÑeÒØiÒg gÓ Ó d ×eaÖch Ô eÖfÓÖÑaÒce ´ÓfØeÒ cÓÑÔaÖabÐe ØÓ fÔB ¹ÌÖee×µ¸ · fÔB ¹ÌÖee×: ´iµ di×k¹¬Ö×Ø aÒd ´iiµ cache¹¬Ö×غ ÁÒ Øhe di×k¹ iØ ×Ù«eÖ× fÖÓÑ Ô Ó ÓÖ ÙÔ daØe Ô eÖfÓÖÑaÒceº A× ÔaÖØ Óf fÙØÙÖe · ¬Ö×Ø aÔÔÖÓach¸ Ûe ×ØaÖØ ÛiØh a di×k¹ÓÔØiÑiÞed B ¹ÌÖee¸ bÙØ diÖecØiÓÒ׸ ÄÓÑeØ [½6] ha× iÒdeÔ eÒdeÒØÐÝ adÚÓ caØed bÖeak¹ · ØheÒ ÓÖgaÒiÞe Øhe keÝ× aÒd Ô ÓiÒØeÖ× ÛiØhiÒ each Ôage¹×iÞed iÒg ÙÔ B ¹ÌÖee di×k Ôage× iÒØÓ cache¹fÖieÒdÐÝ ÙÒiØ׸ Ô ÓiÒع ÒÓ de a× a ×ÑaÐÐ ØÖeeº Ìhi× iÒ¹Ôage ØÖee i× a ÚaÖiaÒØ Óf Øhe iÒg ÓÙØ Øhe chaÐÐeÒge× Óf ¬ÒdiÒg aÒ ÓÖgaÒiÞaØiÓÒ ØhaØ ×ØÖike× · ÔÖefeØchiÒg B ¹ÌÖeeº ÌÓ Ôack ÑÓÖe keÝ× aÒd Ô ÓiÒØeÖ× iÒØÓ a gÓ Ó d baÐaÒce b eØÛeeÒ ×eaÖch aÒd iÒ×eÖØiÓÒ Ô eÖfÓÖÑaÒce¸ · aÒ iÒ¹Ôage ØÖee¸ Ûe Ù×e ×hÓÖØ iÒ¹Ôage Ó«×eØ× ÖaØheÖ ØhaÒ fÙÐÐ ×ØÓÖage ÙØiÐiÞaØiÓÒ¸ aÒd ×iÑÔÐiciØݺ Ïe b eÐieÚe ØhaØ fÔB ¹ Ô ÓiÒØeÖ× iÒ aÐÐ bÙØ Øhe Ðeaf ÒÓ de× Óf aÒ iÒ¹Ôage ØÖeeº Ïe aÐ×Ó ÌÖee× achieÚe Øhi× baÐaÒceº GÖaefe aÒd ÄaÖ×ÓÒ [½½] ÔÖe×eÒØed ×hÓÛ Øhe adÚaÒØage× Óf Ù×iÒg di«eÖeÒØ ×iÞe× fÓÖ Ðeaf ÚeÖ×Ù× a ×ÙÖÚeÝ Óf ØechÒiÕÙe× fÓÖ iÑÔÖÓÚiÒg Øhe CÈÍ cache Ô eÖfÓÖ¹ · ÒÓÒ¹Ðeaf ÒÓ de× iÒ aÒ iÒ¹Ôage ØÖeeº ÁÒ cÓÒØÖa×ظ Øhe cache¹ ÑaÒce Óf B ¹ÌÖee iÒdeÜe׺ ÌheÝ di×cÙ××ed a ÒÙÑb eÖ Óf Øech¹ · ¬Ö×Ø aÔÔÖÓach ×ØaÖØ× ÛiØh a cache¹ÓÔØiÑiÞed ÔÖefeØchiÒg B ¹ ÒiÕÙe׸ ×Ùcha×keÝ cÓÑÔÖe××iÓÒ¸ ØhaØ aÖe cÓÑÔÐeÑeÒØaÖÝ ØÓ · ÌÖee ´igÒÓÖiÒg di×k Ôage b ÓÙÒdaÖie×µ¸ aÒd ØheÒ aØØeÑÔØ× ØÓ ÓÙÖ ×ØÙdݸ aÒd cÓÙÐd b e iÒcÓÖÔ ÓÖaØed iÒØÓ fÔB ¹ÌÖee׺ BeÒ¹ · gÖÓÙÔ ØÓgeØheÖ Øhe×e ×ÑaÐÐeÖ ÒÓ de× iÒØÓ Ôage¹×iÞed ÒÓ de× deÖ eØ aк [4] ÔÖe×eÒØ a ÖecÙÖ×iÚeB ¹ÌÖee ×ØÖÙcØÙÖe ØhaØ i× ØÓ ÓÔØiÑiÞe di×k Ô eÖfÓÖÑaÒceº ËÔ eci¬caÐÐݸ Øhe cache¹¬Ö×Ø a×ÝÑÔØÓØicaÐ ÐÝ ÓÔØiÑaи ÖegaÖdÐe×× Óf Øhe cache ÐiÒe ×iÞe× aÒd aÔÔÖÓach ×eek× ØÓ ÔÐace a ÔaÖeÒØ aÒd iØ× chiÐdÖeÒ ÓÒ Øhe di×k Ôage ×iÞe׸ bÙØ a××ÙÑiÒg ÒÓ ÔÖefeØchiÒgº ×aÑe Ôage¸ aÒd ØÓ ÔÐace adjaceÒØ Ðeaf ÒÓ de× ÓÒ Øhe ×aÑe ÅaiÒØaiÒiÒg b ÓØh ×ØÖÙcØÙÖe× a× ÒeÛ keÝ× aÖe added Ôageº 1.3 Contributions of This Paper aÒd ÒÓ de× ×ÔÐiØ Ô Ó×e× ÔaÖØicÙÐaÖ chaÐÐeÒge׺ Ïe ÛiÐÐ ×hÓÛ Ìhi× ÔaÔ eÖ Ñake× Øhe fÓÐÐÓÛiÒg cÓÒØÖibÙØiÓÒ׺ FiÖ×ظ Ûe · · hÓÛ ØÓ ÔÖÓ ce×× iÒ×eÖØiÓÒ× aÒd deÐeØiÓÒ× eÆcieÒØÐÝ iÒ b ÓØh ÔÖÓÔ Ó×e aÒd eÚaÐÙaØe FÖacØaÐ ÈÖefeØchiÒg B ¹ÌÖee× ´fÔB ¹ · di×k¹¬Ö×Ø aÒd cache¹¬Ö×Ø fÔB ¹ÌÖee׺ Ïe ×eÐecØ Øhe ÓÔØiÑaÐ ÌÖee×µ a× a ÒÓÚeÐ iÒdeÜ ×ØÖÙcØÙÖe ØhaØ ÓÔØiÑiÞe× b ÓØh cache ÒÓ de ×iÞe× iÒ b ÓØh aÔÔÖÓache× ØÓ ÑaÜiÑiÞe Øhe ÒÙÑbeÖ Óf aÒd di×k Ô eÖfÓÖÑaÒce ×iÑÙÐØaÒeÓÙ×Ðݺ ËecÓÒd¸ Ûe ÔÖe×eÒØ eÒØÖÝ ×ÐÓØ× iÒ a Ðeaf Ôage ÛhiÐe aÒaÐÝØicaÐÐÝ achieÚiÒg ×eaÖch deØaiÐed aÒaÐÝ×i× Óf Øhe fÙÒdaÑeÒØaÐ ØÖadeÓ«× b eØÛeeÒ Øhe · cache Ô eÖfÓÖÑaÒce ÛiØhiÒ ½¼± Óf Øhe b e×غ di×k¹¬Ö×Ø aÒd Øhe cache¹¬Ö×Ø iÑÔÐeÑeÒØaØiÓÒ× Óf fÔB ¹ÌÖee׺ ÁdeaÐÐݸ b ÓØh Øhe di×k¹¬Ö×Ø aÒd Øhe cache¹¬Ö×Ø aÔÔÖÓache× ÏhiÐe Øhe Ô eÖfÓÖÑaÒce Óf each Óf Øhe×e iÑÔÐeÑeÒØaØiÓÒ× ÛÓÙÐd achieÚe ideÒØicaÐ daØa ÐaÝÓÙØ׸ aÒd heÒce eÕÙiÚaÐeÒØ ÖeÑaiÒ× ×ÐighØÐÝ bia×ed ØÓÛaÖd iØ× ÓÖigiÒaÐ gÓaи b ÓØh ÚeÖ¹ · cache aÒd Á»Ç Ô eÖfÓÖÑaÒceº ÁÒ ÔÖacØice¸ hÓÛeÚeÖ¸ Øhe Ñi×¹ ×iÓÒ× Óf fÔB ¹ÌÖee× iÑÔÖÓÚe ÙÔ ÓÒ Øhe cache Ô eÖfÓÖÑaÒce · ÑaØch ØhaØ aÐÑÓ×Ø aÐÛaÝ× Ó ccÙÖ× b eØÛeeÒ Øhe ×iÞe Óf a cache¹ Óf di×k¹ÓÔØiÑiÞed B ¹ÌÖee× ´ÛiØhÓÙØ ×igÒi¬caÒØÐÝ degÖadiÒg ÓÔØiÑiÞed ×ÙbØÖee aÒd Øhe ×iÞe Óf a di×k Ôage ´iÒ addiØiÓÒ Á»Ç Ô eÖfÓÖÑaÒceµ
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