Compressed Tree Representations

The problem is, given a tree, to encode it compactly so that basic operations on the tree are done quickly, preferably in constant time for static trees. Here, we consider the most basic class of trees: rooted ordered unlabeled trees. The information-theoretic lower bound for representing an n-node ordered tree is 2n o.n/ bits because there are 2n 2 n 1 =n different trees. Therefore, the aim is to encode an ordered tree in 2nC o.n/ bits including auxiliary data structures so that basic operations are done quickly. We assume that the computation model is the .logn/-bit word RAM, that is, memory access for consecutive .logn/ bits and arithmetic and logical operations on two .log n/-bit integers are done in constant time.

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