Representation of ordered trees with a given degree distribution

Abstract

The degree distribution of an ordered tree T with n nodes is n→=(n0,…,nn−1), where ni is the number of nodes in T with i children. Let N(n→) be the number of trees with degree distribution n→. We give a data structure that stores an ordered tree T with n nodes and degree distribution n→ using log⁡N(n→)+O(n/logt⁡n) bits for every constant t. The data structure answers tree queries in constant time. Our data structure has improved space complexity compared to the known data structures for ordered trees with lowest space complexity: The structure of Jansson et al. [14] that uses log⁡N(n→)+O(nlog⁡log⁡n/log⁡n) bits, and the structure of Navarro and Sadakane [18] that uses 2n+O(n/logt⁡n) bits for every constant t.