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\section{Challenegs in Bushy Tree Implementation}  Moving from left-deep tree to a Bushy tree is a challenge as the number of possible structures in bushy trees are much larger. Left-deep trees have only one structure regardless of the number of attributes involved. Therefor the number of possible permutations are N! . But for bushy trees possible number of structures are given by   $$S(N) $$f(x)  = \begin{cases} 1 0 &  \text{if $ N = $0 < x \le 0.05$}; \\  0.1 & \text{if $0.05 < x \le  1$}; \\ $\displaystyle \sum_{i=1}^{N} \frac{1}{n}$ 0.2 &  \text{if $N \ne 0$}  2 $1 < x \le 5$};\\  2^{\frac{x}{20}} &  \text{if $ N = 1$}.\end{cases}$$ $5 < x \le 100$};.\end{cases} $$  Therefore the number of possible permutations are $S(N)*N!$. Unlike left-deep tree case, estimating the cost for all the possible bushy trees is computationally infeasible for moderately large N. Therefore it is required to come with a heuristic to select set of permutations for cost computations.Some heuristics considered are