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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   $$ S(N) = \begin{cases}   1 & \text{if $N = 1$}; \\  \sum_{i=1}^{N} & \text{if $N \ne 0$} $$ \\  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