Practical Wavelet Tree Construction

Dinklage, Patrick; Ellert, Jonas; Fischer, Johannes; Kurpicz, Florian; Löbel, Marvin

doi:10.1145/3457197

Cited by 9 publications

(6 citation statements)

References 41 publications

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“…The algorithm is also suitable for wavelet matrices and is suitable for large alphabet variants. Although the algorithm works well with wavelet matrices and is particularly suitable for large alphabet variants, its computational complexity can increase with the amount of data, which may limit its application when dealing with extremely large data sets [13]. Malmir I proposed a new method based on quadratic programming wavelet.…”

Section: Related Workmentioning

confidence: 99%

“…L 1 is the input voltage stabilizing inductance. Eq (13) represents the circuit equation under modal conditions.…”

Section: Plos Onementioning

confidence: 99%

“…In Eq (13), L m represents the excitation inductance of the high-frequency transformer. N 1 and N 2 are the primary winding turns and secondary winding turns of high-frequency transformer, respectively.…”

Section: Plos Onementioning

confidence: 99%

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Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms

2024

PLoS ONE

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In power electronics systems, system design and operation often involve multiple time and space scales, ranging from nanosecond switching dynamics to hour-level system operation behavior. Due to the complexity of these systems and the rise of wide-gap semiconductor technology, a series of multi-scale phenomena have emerged that are difficult to ignore. The high frequency of switching operations makes multi-scale effects particularly significant, including the fast dynamic response of the power loop, EMI, and heat conduction problems. They are key factors that must be considered in the design to ensure the efficient and reliable operation of power electronic devices. This study proposes the construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms to address the multi-scale phenomenon and limitations of single-scale power electronic converters. Firstly, a joint scale model for power electronic converters at both macro and micro-scales was established, targeting both single-scale models and simple combinations of multiple scale models for power electronic converters. The traditional single-scale model is sufficient to describe the average behavior of the converter, but it has serious limitations in capturing fast transient processes and high-frequency switching behavior in power electronic systems. These limitations often manifest themselves when there is a need to capture fine timescales of detail. By transforming between the time domain and the frequency domain, wavelet decomposition enables the model to capture both macroscopic average characteristics and microscopic transient dynamics. The wavelet reconstruction algorithm can simulate all kinds of fast changes in the actual working process more accurately and compress irrelevant information while retaining key signal features, so as to optimize the simulation performance of the model. Secondly, this algorithm is used to analyze BC in short time scale. Finally, the short time scale characteristics of power electronic converters are analyzed. Experimental results show that the fusion of wavelet decomposition and reconstruction algorithm enhances the accuracy of the power electronic converter model and improves the performance of the system. The model achieves an error reduction of nearly 3% in the calculation step size of 10-7s, which has a significant impact on the high precision requirements of high-frequency operations. In addition, the optimal calculation step size of 8×10-8s achieves an error reduction of more than 14%, making an important contribution to the transient analysis and fine structure simulation. The wavelet algorithm can improve the accuracy of multi-scale modeling in power electronic system and reduce the simulation time. The reduction of error not only shows the improvement of the accuracy of the model, but also shows its practical significance in the design and test of the actual power electronic system. The reduction in error reveals the ability to more accurately predict and mitigate potential performance problems in matching tests with actual hardware, as well as its ability to adapt to emerging wide bandgap semiconductor materials and structures.

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Section: Related Workmentioning

confidence: 99%

“…L 1 is the input voltage stabilizing inductance. Eq (13) represents the circuit equation under modal conditions.…”

Section: Plos Onementioning

confidence: 99%

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Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms

2024

PLoS ONE

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“…In shared memory, wavelet trees can be computed in O(σ +log n) time requiring only O(n log σ/ √ log n) work [39]. In practice, the fastest construction algorithms are based on domain decomposition [27,17], where partial wavelet trees are computed in parallel and are then merged also in parallel, using a bottom-up construction for the partial wavelet tree construction [9]. Wavelet trees can also be computed in other models of computation, e.g., distributed memory [10] and external memory [12].…”

Section: Preliminariesmentioning

confidence: 99%

Faster Wavelet Trees with Quad Vectors

Ceregini¹,

Kurpicz²,

Venturini³

2023

Preprint

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Given a text, rank and select queries return the number of occurrences of a character up to a position (rank) or the position of a character with a given rank (select). These queries have applications in, e.g., compression, computational geometry, and pattern matching in the form of the backwards search-the backbone of many compressed full-text indices. A wavelet tree is a compact data structure that for a text of length n over an alphabet of size σ requires only n log σ (1 + o( 1)) bits of space and can answer rank and select queries in Θ(log σ) time. Wavelet trees are used in the applications described above.In this paper, we show how to improve query performance of wavelet trees by using a 4-ary tree instead of a binary tree as basis of the wavelet tree. To this end, we present a space-efficient rank and select data structure for quad vectors. The 4-ary tree layout of a wavelet tree helps to halve the number of cache misses during queries and thus reduces the query latency. Our experimental evaluation shows that our 4-ary wavelet tree can improve the latency of rank and select queries by a factor of ≈ 2 compared to the wavelet tree implementations contained in the widely used Succinct Data Structure Library (SDSL). ACM Subject ClassificationTheory of computation → Data structures design and analysis; Applied computing → Document management and text processing; Applied computing → Document searching

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“…Bit vectors are building blocks of many important compact and succinct data structures like wavelet trees [10] that have applications in many compressed fulltext indices (e.g., the FM-index [10] and r-index [11]; we point to the following surveys [6,9,17,18] for more information on wavelet trees), succinct graph representations (e.g., LOUDS [14]), and can also be used as a representation of monotonic sequences of integers (e.g., Elias-Fano coding [7,8]) that supports predecessor queries. It should be noted that all of the applications mentioned above require rank and/or select queries on bit vectors.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Engineering Compact Data Structures for Rank and Select Queries on Bit Vectors

Kurpicz

2022

Lecture Notes in Computer Science

Self Cite

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Bit vectors are fundamental building blocks of succinct data structures used in compressed text indices, e.g., in the form of the wavelet trees. Here, two types of queries are of interest: rank and select queries. In practice, the smallest (uncompressed) rank and select data structure cs-poppy has a space overhead of $$\approx $$ ≈ 3.51 % [Zhou et al. SEA 2013] [26]. Using the same overhead, we present a data structure that can answer queries up to 8 % (rank) and 16.5 % (select) faster compared with cs-poppy.

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Practical Wavelet Tree Construction

Cited by 9 publications

References 41 publications

Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms

Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms

Faster Wavelet Trees with Quad Vectors

Engineering Compact Data Structures for Rank and Select Queries on Bit Vectors

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