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\title{Algorithm for listing all hypotheses that statisfy a quality check}
\date{25th January, 2010}
\author{Pratik Jawanpuria}
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\noindent\Large{Problem Statement}:
\newline
\\Given data `D':
\newline
\\\begin{tabular}{|c|c|}
\hline
Transaction ID & Items \\
\hline
1 & \{D,O,N,K,E,Y\} \\
\hline
2 & \{M,O,N,K,E,Y\} \\
\hline
3 & \{M,A,K,E\} \\
\hline
4 & \{M,U,C,K,Y\} \\
\hline
5 & \{C,O,O,K,I,E\} \\
\hline
\end{tabular}
\newline
\\\Large{$\Sigma$} = \{A, C, D, E, I, K, M, N, O, U, Y\}
\newline
\\Find all hypothesis, \emph{h}, satisfying:
$Q_{D}$ = $\frac{|covers_{D}(h)|}{|D|}$ $\geq$ 0.6
\newline
\\Brute Force Algorithm
\begin{enumerate}
\item Enumerate all the subsets of \Large{$\Sigma$} (which will be \Large{$2^{\Sigma}$})
\item $\forall$ h $\epsilon$ \Large{$2^{\Sigma}$}, check if $Q_{D}$ = $\frac{|covers_{D}(h)|}{|D|}$ $\geq$ 0.6 is true
\end{enumerate}
Observation
\begin{enumerate}
\item This algo does not account for the properties of $Q_{D}$
\item This algo does not apply understanding of the structure of search space
\end{enumerate}
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