. ▁ ▁Given ▁that ▁the ▁resulting ▁hash ▁tables ▁have ▁only ▁ ▁non - zero ▁entries , ▁one ▁can ▁reduce ▁the ▁amount ▁of ▁memory ▁used ▁per ▁each ▁hash ▁table ▁to ▁ ▁using ▁standard ▁hash ▁functions . ▁ ▁Given ▁a ▁query ▁point ▁, ▁the ▁algorithm ▁iter ates ▁over ▁the ▁ ▁hash ▁functions ▁. ▁ ▁For ▁each ▁ ▁considered , ▁it ▁retr ieves ▁the ▁data ▁points ▁that ▁are ▁hash ed ▁into ▁the ▁same ▁bucket ▁as ▁. ▁ ▁The ▁process ▁is ▁stopped ▁as ▁soon ▁as ▁a ▁point ▁within ▁distance ▁ ▁from ▁ ▁is ▁found . ▁ ▁Given ▁the ▁parameters ▁ ▁and ▁, ▁the ▁algorithm ▁has ▁the ▁following ▁performance ▁guarante es : ▁ ▁pre processing ▁time : ▁, ▁where ▁ ▁is ▁the ▁time ▁to ▁evaluate ▁a ▁function ▁ ▁on ▁an ▁input ▁point ▁; ▁ ▁space : ▁, ▁plus ▁the ▁space ▁for ▁storing ▁data ▁points ; ▁ ▁query ▁time : ▁; ▁ ▁the ▁algorithm ▁succeed s ▁in ▁finding ▁a ▁point ▁within ▁distance ▁ ▁from ▁ ▁( if ▁there ▁exists ▁a ▁point ▁within ▁distance ▁) ▁with ▁probability ▁at ▁least ▁; ▁ ▁For ▁a ▁fixed ▁approximation ▁ratio ▁ ▁and ▁prob abilities ▁ ▁and ▁, ▁one ▁can ▁set ▁ ▁and ▁, ▁where ▁. ▁Then ▁one ▁obtain s ▁the ▁following ▁performance ▁guarante es : ▁ ▁pre processing ▁time : ▁; ▁ ▁space : ▁, ▁plus ▁the ▁space ▁for ▁storing ▁data ▁points ; ▁ ▁query ▁time : ▁; ▁ ▁See ▁also ▁Blo om ▁filter ▁Cur se ▁of ▁dimensional ity ▁Fe ature ▁has hing ▁Fourier - related ▁transform s ▁Ge oh ash ▁Mult il ine