Compressed Range Minimum Queries

Jo, Seungbum; Mozes, Shay; Weimann, Oren

doi:10.1007/978-3-030-00479-8_17

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…We consider three representations of the tree shape: (1) an augmented balanced-parentheses (BP) representation occupying roughly 2 n + o ( n ) bits [10] and answering queries in constant time; (2) a simple DAG-compressed representation (with each non-terminal storing the size of its expansion) answering queries in time bounded by its height; and (3) an interval-tree storing selected intervals corresponding to nodes in the Cartesian tree and answering queries in constant time. We do not include Gawrychowski et al’s compressed RMQ data structure [14] because we are not aware of an implementation and we see no easy way to estimate its space usage for the divergence array.…”

Section: Components: Building Blocks For a Pbwt Data Structurementioning

confidence: 99%

Compressed Data Structures for Population-Scale Positional Burrows–Wheeler Transforms

Bonizzoni

Boucher

Cozzi

et al. 2022

Preprint

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The positional Burrows–Wheeler Transform (PBWT) was presented in 2014 by Durbin as a means to find all maximal haplotype matches in h sequences containing w variation sites in O(hw)-time. This time complexity of finding maximal haplotype matches using the PBWT is a significant improvement over the naïve pattern-matching algorithm that requires O(h2w)-time. Compared to the more famous Burrows-Wheeler Transform (BWT), however, a relatively little amount of attention has been paid to the PBWT. This has resulted in less space-efficient data structures for building and storing the PBWT. Given the increasing size of available haplotype datasets, and the applicability of the PBWT to pangenomics, the time is ripe for identifying efficient data structures that can be constructed for large datasets. Here, we present a comprehensive study of the memory footprint of data structures supporting maximal haplotype matching in conjunction with the PBWT. In particular, we present several data structure components that act as building blocks for constructing six different data structures that store the PBWT in a manner that supports efficiently finding the maximal haplotype matches. We estimate the memory usage of the data structures by bounding the space usage with respect to the input size. In light of this experimental analysis, we implement the solutions that are deemed to be superior with respect to the memory usage and show the performance on haplotype datasets taken from the 1000 Genomes Project data.

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Section: Components: Building Blocks For a Pbwt Data Structurementioning

confidence: 99%

Compressed Data Structures for Population-Scale Positional Burrows–Wheeler Transforms

Bonizzoni

Boucher

Cozzi

et al. 2022

Preprint

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“…Again, for the random permutations considered here, this would not result in space reductions. Recently, Jo, Mozes and Weimann [19] designed RMQ solutions for grammar-compressed input arrays resp. DAG-compressed Cartesian trees.…”

Section: Related Workmentioning

confidence: 99%

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

Munro¹,

Wild²

2019

Preprint

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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).1 To simplify the presentation, we assume the elements in A are unique. In the general case, we fix a tie-breaking rule, usually to return the leftmost minimum. Our data structures extend to any such convention.

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Efficient Algorithms for Range Mode Queries in the Big Data Era

Karras,

Theodorakopoulos,

Karras

et al. 2024

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The mode is a fundamental descriptive statistic in data analysis, signifying the most frequent element within a dataset. The range mode query (RMQ) problem expands upon this concept by preprocessing an array A containing n natural numbers. This allows for the swift determination of the mode within any subarray A[a..b], thus optimizing the computation of the mode for a multitude of range queries. The efficacy of this process bears considerable importance in data analytics and retrieval across diverse platforms, including but not limited to online shopping experiences and financial auditing systems. This study is dedicated to exploring and benchmarking different algorithms and data structures designed to tackle the RMQ problem. The goal is to not only address the theoretical aspects of RMQ but also to provide practical solutions that can be applied in real-world scenarios, such as the optimization of an online shopping platform’s understanding of customer preferences, enhancing the efficiency and effectiveness of data retrieval in large datasets.

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Compressed Range Minimum Queries

Cited by 3 publications

References 14 publications

Compressed Data Structures for Population-Scale Positional Burrows–Wheeler Transforms

Compressed Data Structures for Population-Scale Positional Burrows–Wheeler Transforms

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

Efficient Algorithms for Range Mode Queries in the Big Data Era

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