Entropy Trees and Range-Minimum Queries In Optimal Average-Case Space



Munro, J Ian and Wild, Sebastian ORCID: 0000-0002-6061-9177
(2019) Entropy Trees and Range-Minimum Queries In Optimal Average-Case Space. [Report]

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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 $2n+o(n)$ 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 $1.736n+o(n)$ 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).

Item Type: Report
Uncontrolled Keywords: cs.DS, cs.DS
Depositing User: Symplectic Admin
Date Deposited: 15 Aug 2019 14:39
Last Modified: 19 Jan 2023 00:29
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3051855