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We present a new universal source code for distributions of unlabeled binaryand ordinal trees that achieves optimal compression to within lower order termsfor all tree sources covered by existing universal codes. At the same time, itsupports answering many navigational queries on the compressed representationin constant time on the word-RAM; this is not known to be possible for anyexisting tree compression method. The resulting data structures, "hypersuccincttrees", hence combine the compression achieved by the best known universalcodes with the operation support of the best succinct tree data structures. Weapply hypersuccinct trees to obtain a universal compressed data structure forrange-minimum queries. It has constant query time and the optimal worst-casespace usage of $2n+o(n)$ bits, but the space drops to $1.736n + o(n)$ bits onaverage for random permutations of $n$ elements, and $2\lg\binom nr + o(n)$ forarrays with $r$ increasing runs, respectively. Both results are optimal; theformer answers an open problem of Davoodi et al. (2014) and Golin et al.(2016). Compared to prior work on succinct data structures, we do not have totailor our data structure to specific applications; hypersuccinct treesautomatically adapt to the trees at hand. We show that they simultaneouslyachieve the optimal space usage to within lower order terms for a wide range ofdistributions over tree shapes, including: binary search trees (BSTs) generatedby insertions in random order / Cartesian trees of random arrays, randomfringe-balanced BSTs, binary trees with a given number of binary/unary/leafnodes, random binary tries generated from memoryless sources, full binarytrees, unary paths, as well as uniformly chosen weight-balanced BSTs, AVLtrees, and left-leaning red-black trees.

Hypersuccinct Trees -- New universal tree source codes for optimal compressed tree data structures and range minima