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\subsection{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 tables involved. Therefor the number of possible permutations are N! . But for bushy trees possible number of structures are given by \\  $$ S(N) = 1 if N $N  \ = \ 1 1$ $$  \\   $$  S(N) = $\displaystyle \displaystyle  \sum_{N=1}^{i} (N)(N-i)$ (N)(N-i)  \ $  if\  N > 1 1$  $$\\ 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 (~7). Therefore it is required to come with a heuristic to select set of permutations for cost computations.  \subsection{Heuristics to Select Bushy Trees}