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Bhathiya edited section_Challenegs_in_Bushy_Trees__.tex
about 8 years ago
Commit id: 81eed4ed240fc4d5dc97e64440afd4e7ec5caff4
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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) = 1 if $N = 1 $ \\
S(N) = $\displaystyle \sum_{N=1}^{i}
\(N){N-i}$ (N){N-i}$ if N > 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. Therefore it is required to come with a heuristic to select set of permutations for cost computations.Some heuristics considered are