Commit 9744cd1b by Parth Mittal

### typset algorithm better

parent 5d2b3d02
 ... ... @@ -42,18 +42,16 @@ of each element in a stream of integers. We shall see that it also provides us with a small set $C$ containing $F_k$, and hence lets us solve the frequent elements problem efficiently. TODO: Typeset the algorithm better. \proc{FrequencyEstimate}$(\alpha, k)$ \algo{FrequencyEstimate} \algalias{Misra/Gries Algorithm} \algin the data stream $\alpha$, the target for the estimator $k$ \:\em{Init}: $A \= \emptyset$. (an empty map) \:\em{Init}: $A \= \emptyset$. \cmt{an empty map} \:\em{Process}($x$): \: If $x \in$ keys($A$), $A[x] \= A[x] + 1$. \: Else If $\vert$keys($A$)$\vert < k - 1$, $A[x] \= 1$. \: Else \::If $x \in$ keys($A$), $A[x] \= A[x] + 1$. \::Else If $\vert$keys($A$)$\vert < k - 1$, $A[x] \= 1$. \::Else \forall $a \in$~keys($A$): $A[a] \= A[a] - 1$, delete $a$ from $A$ if $A[a] = 0$. \:\em{Output}: $\hat{f}_a = A[a]$ If $a \in$~keys($A$), and $\hat{f}_a = 0$ otherwise. \algout $\hat{f}_a = A[a]$ If $a \in$~keys($A$), and $\hat{f}_a = 0$ otherwise. \endalgo Let us show that $\hat{f}_a$ is a good estimate for the frequency $f_a$. ... ... @@ -95,6 +93,10 @@ $\vert C \vert = \vert$keys($A$)$\vert \leq k - 1$, and a key-value pair can be stored in $\O(\log n + \log m)$ bits. \qed \subsection{The Count-Min sketch} We will now look at a randomized streaming algorithm that performs the same task \endchapter ... ...
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