Hitters Heavy stream of Its e g IP addresses a ay ay 64 each 2 n c ex ai n For any ten true t f let ett tires in appears 9,92 at a ffrequency Goal f allelts Fa return set x large using of t space fxt Tz heavy halters add to list If of sub linear space with Provably impossible Modified goal list Yz add it to fx If w p f fxtsnz En l list then added to s If x F Lto 4 Ee 20 E 0.01 Suppose on list of HH is definitely fx If x 2 0.08N then with prob 31 Lto if x added to list f O 04h En 01h Yz o.O 5h o Modified goal list Yz add it to fx If w p f fxtsnz list l then added to s Engg If x Count Min Sketch use elegant very simple data stmche I s e des l
K o e designer specifies Count Min Sketch bye each of size b 2D hash tables l keep array i b 4YIIsepae hashtable i no i i 5 e he e ett shows when up tf CMS j jel hj xD IncCx increment is at any tinet fit Observation V j hjk omg tx County hjlxD Cms Cj return min is's El if Countfx Fc by ObsuralnLO Couth to HH list add hasi Assump behave like random maps in the following sense hashfus V xfgyc LDV tb lejelprfhjlxfh.ly El hashas I are indep geochotm Analysis t Fix elt X the 2j3f Zj Define zj fxttff.gg Yq w.j q.e hjcxi hjlD
is o aw e fxtttbefxtth f tty fytE wxy E 2j bprfhjcxj ten hg.ly t b E 2J fxt IF MaskaisInegu X Markov's Inga is 2 2 n v By a nonnegative et Prix xECxD L Prf 2J Ext 2 p at castzo 3fxtt2I yeuntzbEl PY.FI 2e Ze fxtt Prf2,3fxtt2f 223k 25 fxtt2f Prey fifty Pr Prue fxtt2Ib 2 indef ghashby by I 7 Mdgs of 2J's s fxtt 2mg Pr 1 County E 2h W Z min I T I ee En I Modified goal K or E add it to list Yz f If x added to list l f fxtsnz then w p s If Engg 8 122 En 2hbE l eogff 2zf b
6 200 E Fo 5 e o.O I 5 b 432 error prob is I 004N has f so 04h if output definitely f 37z En ifontputx thnwitnprob 3152 004N 0.0in prime number n p to 03in hcxt fext gfmodpmodbffzee.IT H g H1 pcp c universal family next t.is mdPmdbI 93 h If is chosen uniformly atranderm from Jt V x fyprfhc.no bt hcg T heft
Markov's Inequality X nonnegative For any positivecast n v c CEH Pr X E z Prog F G t.EE H 15 O EcECX Z Pr t X x X CECX Pr X CECH cECx tf XxcECx pr
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