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txrManor MendelAssaf Naor% Esrc:107RamseyProximity.tex3
txbAbstractT*`src:109RamseyProximity.tex2+|
txrThisnpapermaddressestwfoproblemslyingattheintersectionofgeometricanalysisandtheoretical `computer
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thattheeٙxistenceofgoodRamseٙypartitionsimpliesasolutiontothemetricRamseٙy`problem
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txsy2(0;1),evٙeryn-pointmetricspacehasasubsetofsize`n^4+|
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txmi"PwhichШembedsЧintoHilbertspacewithdistortionO(1=").Thisresultisbestpossibleandimproٙves`partxofythemetricRamseٙytheoremofBartal,Linial,MendelxandNaor[html:5 html: ],inadditiontoconsiderably`simplifying.its.proof.%W33euseourne wRamseٙypartitionstodesignapproximatedistanceoracleswith`aBuni vٙersalAconstantquerytime,closingag3apleftopenbyThorupandZwickin[html:32 html:
].^NamelyY,we`sho wthatforevٙerynpointmetricspaceXp,andkE21,thereeٙxistsanO(k+)-approximatedistanceoracle
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