Predecessor Search

Navarro, Gonzalo; Rojas-Ledesma, Javiel

doi:10.1145/3409371

Cited by 16 publications

(7 citation statements)

References 65 publications

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“…, δ. We use the structure of [30, Appendix A] giving a query time of O(log log w u δ ), where w is the word size, but there are many other possible trade-offs [43] that we skip for simplicity of exposition. Furthermore, in each marked block S q at any level ℓ except the first and the last ones, we store a sample of A corresponding to the last element of S q to be able to descend to the correct child.…”

Section: Supporting Rank Queriesmentioning

confidence: 99%

Compressing and Querying Integer Dictionaries Under Linearities and Repetitions

2022

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We revisit the fundamental problem of compressing an integer dictionary that supports efficient rank and select operations by exploiting simultaneously two kinds of regularities arising in real data: repetitiveness and approximate linearity. We attack this problem by proposing two novel compressed indexing approaches that extend the classic Lempel-Ziv compression scheme and the more recent block tree data structure with new algorithms and data structures that allow them to also capture regularities in terms of the approximate linearity in the data. Finally, we corroborate these theoretical results with a wide set of experiments on real and synthetic datasets, which allow us to show that our approaches achieve new interesting space-time trade-offs that characterise them as more robust in most practical scenarios compared to the known data structures that exploit only one of the two regularities.INDEX TERMS Compressed data structures, Data compression, Entropy.

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Section: Supporting Rank Queriesmentioning

confidence: 99%

Compressing and Querying Integer Dictionaries Under Linearities and Repetitions

2022

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“…In update one can insert/delete integers to/from set S. During query, for a given integer x one should returns the largest integer y ∈ S such that x y. Predecessor problem is a well-studied problem both in terms of lower and upper bounds (see the recent survey [35]). In word-RAM the complexity of Predecessor operations is well understood to be…”

Section: Computation Modelmentioning

confidence: 99%

Dynamic data structures for parameterized string problems

Olkowski¹,

Pilipczuk²,

Rychlicki³

et al. 2022

Preprint

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We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently, our goal is to design a data structure that efficiently maintains a solution, or reports a lack thereof, upon updates in the instance.We first consider the Closest String problem, for which we design randomized dynamic data structures with amortized update times d O(d) and |Σ| O(d) , respectively, where Σ is the alphabet and d is the assumed bound on the maximum distance. These are obtained by combining known static approaches to Closest String with color-coding.Next, we note that from a result of Frandsen et al. [J. ACM'97] one can easily infer a metatheorem that provides dynamic data structures for parameterized string problems with worstcase update time of the form O k (log log n), where k is the parameter in question and n is the length of the string. We showcase the utility of this meta-theorem by giving such data structures for problems Disjoint Factors and Edit Distance. We also give explicit data structures for these problems, with worst-case update times O(k2 k log log n) and O(k 2 log log n), respectively. Finally, we discuss how a lower bound methodology introduced by Amarilli et al. [ICALP'21] can be used to show that obtaining update time O(f (k)) for Disjoint Factors and Edit Distance is unlikely already for a constant value of the parameter k.

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“…In the legend, US stands for universe sampling, BV stands for buckets backed by bit vectors, UL for unsorted lists. Missing points indicate throughputs lower than 2 20 operations per second or exceeding of 300 bits consumed per key, respectively, and are omitted for clarity. long as n ′ < θ max .…”

Section: Figurementioning

confidence: 99%

“…It can be considered a generalized form of the membership problem or a simple version of the nearest neighbour problem. Navarro and Rojas-Ledesma [20] recently gave a thorough survey on the topic, recapping the past four decades of research.…”

Section: Introductionmentioning

confidence: 99%

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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Predecessor Search

Cited by 16 publications

References 65 publications

Compressing and Querying Integer Dictionaries Under Linearities and Repetitions

Compressing and Querying Integer Dictionaries Under Linearities and Repetitions

Dynamic data structures for parameterized string problems

Engineering Predecessor Data Structures for Dynamic Integer Sets

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