Practical Range Minimum Queries Revisited

Baumstark, Niklas; Gog, Simon; Heuer, Tobias; Labeit, Julian

doi:10.4230/lipics.sea.2017.12

Cited by 3 publications

(3 citation statements)

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“…They clearly outperform the STL set and for all universes in question, at least one of our data structures is faster than burst tries, the previously fastest known to us. We confirm once more [4,10,11,15] that naïve solutions can be more practical than sophisticated data structures on modern hardware and sufficiently small inputs. We also observed that SIMD instructions, while faster than sequences of classic (SISD) instructions when used in batches, may turn out less useful in more complex scenarios.…”

Section: Discussionsupporting

confidence: 70%

Engineering Predecessor Data Structures for Dynamic Integer Sets

Dinklage¹,

Fischer²,

Herlez³

2021

Preprint

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We present highly optimized data structures for the dynamic predecessor problem, where the task is to maintain a set S of w-bit numbers under insertions, deletions, and predecessor queries (return the largest element in S no larger than a given key). The problem of finding predecessors can be viewed as a generalized form of the membership problem, or as a simple version of the nearest neighbour problem. It lies at the core of various real-world problems such as internet routing.In this work, we engineer (1) a simple implementation of the idea of universe reduction, similar to van-Emde-Boas trees (2) variants of y-fast tries [Willard, IPL'83], and (3) B-trees with different strategies for organizing the keys contained in the nodes, including an implementation of dynamic fusion nodes [Pǎtraşcu and Thorup, FOCS'14]. We implement our data structures for w = 32, 40, 64, which covers most typical scenarios.Our data structures finish workloads faster than previous approaches while being significantly more space-efficient, e.g., they clearly outperform standard implementations of the STL by finishing up to four times as fast using less than a third of the memory. Our tests also provide more general insights on data structure design, such as how small sets should be stored and handled and if and when new CPU instructions such as advanced vector extensions pay off.

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Section: Discussionsupporting

confidence: 70%

Engineering Predecessor Data Structures for Dynamic Integer Sets

Dinklage¹,

Fischer²,

Herlez³

2021

Preprint

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“…Worst-case optimal succinct data structures for the RMQ problem have been presented by Fischer and Heun [21], with subsequent simplifications by Ferrada and Navarro [18] and Baumstark et al [5]. Implementations of (slight variants) of these solutions are part of widely-used programming libraries for succinct data structures, such as Succinct [1] and SDSL [34].…”

Section: A5 Range-minimum Queriesmentioning

confidence: 99%

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

Munro,

Nicholson,

Benkner

et al. 2021

Preprint

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We present a new universal source code for unlabeled binary and ordinal trees that achieves asymptotically optimal compression for all tree sources covered by existing universal codes. At the same time, it supports answering many navigational queries on the compressed representation in constant time on the word-RAM; this is not known to be possible for any existing tree compression method. The resulting data structures, "hypersuccinct trees", hence combine the compression achieved by the best known universal codes with the operation support of the best succinct tree data structures. Compared to prior work on succinct data structures, we do not have to tailor our data structure to specific applications; hypersuccinct trees automatically adapt to the trees at hand. We show that it simultaneously achieves the asymptotically optimal space usage for a wide range of distributions over tree shapes, including: random binary search trees (BSTs) / Cartesian trees of random arrays, random fringe-balanced BSTs, binary trees with a given number of binary/unary/leaf nodes, random binary tries generated from memoryless sources, full binary trees, unary paths, as well as uniformly chosen weight-balanced BSTs, AVL trees, and left-leaning red-black trees. Using hypersuccinct trees, we further obtain the first data structure that answers range-minimum queries on a random permutation of n elements in constant time and using the optimal 1.736n + o(n) bits on average, solving an open problem of Davoodi et al. (2014) andGolin et al. (2016).

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“…Worst-case optimal succinct data structures for the RMQ problem have been presented by Fischer and Heun [9], with subsequent simplifications by Ferrada and Navarro [7] and Baumstark et al [3]. Implementations of (slight variants) of these solutions are part of widely-used programming libraries for succinct data structures, such as Succinct [1] and SDSL [12].…”

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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Practical Range Minimum Queries Revisited

Cited by 3 publications

References 0 publications

Engineering Predecessor Data Structures for Dynamic Integer Sets

Engineering Predecessor Data Structures for Dynamic Integer Sets

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

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

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