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In computer science, a red–black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree hold an extra "color" bit, often drawn as red and black, which help ensure that the tree is always approximately balanced.
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Consider is a given simplex, is a given node corresponding to the last vertex of , is the label associate to that node, is the depth of that node, is the dimension of the simplicial complex, is the maximal number of operations to access in a dictionary (if the dictionary is a red-black tree, = ((())) is the complexity) .