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I am exploring variations of trees. I know that a quality which is sometimes desired is balance in the tree so that tree depth is reduced.

But I am imagining that in situations in which several paths of a tree have to be explored such as in an R-tree, balance might not always be necessarily desired?

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Tree balance is usually preferable as the depth of the tree is shortest and the tree itself is most compact. However, there are few situations in which the fact that is unbalanced is what gives it efficiency. Huffman Coding is an example of this, where shorter paths in a binary tree represent frequently used items.

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