Representation of ordered trees with a given degree distribution

07/01/2018

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by   Dekel Tsur, et al.

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The degree distribution of an ordered tree T with n nodes is n⃗ = (n_0,...,n_n-1), where n_i is the number of nodes in T with i children. Let N(n⃗) be the number of trees with degree distribution n⃗. We give a data structure that stores an ordered tree T with n nodes and degree distribution n⃗ using N(n⃗)+O(n/^t n) bits for every constant t. The data structure answers tree queries in constant time. This improves the current data structures with lowest space for ordered trees: The structure of Jansson et al. [JCSS 2012] that uses N(n⃗)+O(n n/ n) bits, and the structure of Navarro and Sadakane [TALG 2014] that uses 2n+O(n/^t n) bits for every constant t.