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In this paper, we are interested in minimal number of red-nodes in a red-black tree. An ) log ( 2 n n O time dynamic programming algorithm is presented first for computing ) (n s , the smallest number of red internal nodes in a red-black tree on n keys. We then improve the algorithm to a new ) (n O time algorithm. Then the algorithm is improved further to some ) log ( n O time recursive and nonrecursive algorithms. These improved algorithms finally led to a closed-form solution of ) (n s .

On the performance of balance factors of the dichromatic balanced trees for massive data