▁affect ▁the ▁value ▁of ▁the ▁extreme ▁order ▁statistics . ▁ ▁There ▁are ▁other ▁estimation ▁techniques ▁other ▁than ▁min / max ▁sketch es . ▁ ▁The ▁first ▁paper ▁on ▁count - dist inct ▁estimation ▁by ▁F la jo let ▁et ▁al . ▁▁▁ ▁describes ▁a ▁bit ▁pattern ▁sketch . ▁In ▁this ▁case , ▁the ▁elements ▁are ▁hash ed ▁into ▁a ▁bit ▁vector ▁and ▁the ▁sketch ▁holds ▁the ▁logical ▁OR ▁of ▁all ▁hash ed ▁values . ▁The ▁first ▁asympt ot ically ▁space - ▁and ▁time - opt imal ▁algorithm ▁for ▁this ▁problem ▁was ▁given ▁by ▁Daniel ▁M . ▁K ane , ▁J el ani ▁Nelson , ▁and ▁David ▁P . ▁Wood ru ff . ▁ ▁B ottom - m ▁sketch es ▁B ottom - m ▁sketch es ▁▁ ▁are ▁a ▁general ization ▁of ▁min ▁sketch es , ▁which ▁maintain ▁the ▁ ▁minimal ▁values , ▁where ▁. ▁ ▁See ▁Cos ma ▁et ▁al . ▁for ▁a ▁theoretical ▁over view ▁of ▁count - dist inct ▁estimation ▁algorithms , ▁and ▁Met w ally ▁▁ ▁for ▁a ▁practical ▁over view ▁with ▁compar ative ▁simulation ▁results . ▁ ▁We ight ed ▁count - dist inct ▁problem ▁ ▁In ▁its ▁weight ed ▁version , ▁each ▁element ▁is ▁associated ▁with ▁a ▁weight ▁and ▁the ▁goal ▁is ▁to ▁estimate ▁the ▁total ▁sum ▁of ▁weights . ▁Form ally , ▁ ▁Inst ance : ▁A ▁stream ▁of ▁weight ed ▁elements ▁ ▁with ▁repet itions , ▁and ▁an ▁integer ▁. ▁Let ▁ ▁be ▁the ▁number ▁of ▁distinct ▁elements , ▁namely ▁, ▁and ▁let ▁these ▁elements ▁be