Entropy Trees and Range-Minimum Queries In Optimal Average-Case Space
Abstract
The range-minimum query (RMQ) problem is a fundamental data structuring task with numerous applications. Despite the fact that succinct solutions with worst-case optimal bits of space and constant query time are known, it has been unknown whether such a data structure can be made adaptive to the reduced entropy of random inputs (Davoodi et al. 2014). We construct a succinct data structure with the optimal bits of space on average for random RMQ instances, settling this open problem. Our solution relies on a compressed data structure for binary trees that is of independent interest. It can store a (static) binary search tree generated by random insertions in asymptotically optimal expected space and supports many queries in constant time. Using an instance-optimal encoding of subtrees, we furthermore obtain a "hyper-succinct" data structure for binary trees that improves upon the ultra-succinct representation of Jansson, Sadakane and Sung (2012).
Cite
@article{arxiv.1903.02533,
title = {Entropy Trees and Range-Minimum Queries In Optimal Average-Case Space},
author = {J. Ian Munro and Sebastian Wild},
journal= {arXiv preprint arXiv:1903.02533},
year = {2019}
}