Compressed Communication Complexity of Hamming Distance

Mitsuya, Shiori; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki

doi:10.3390/a14040116

Cited by 7 publications

(5 citation statements)

References 14 publications

(22 reference statements)

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“…Our matching upper and lower bounds for the multiplicative sensitivity of γ, which are both 2, improve this existing bound due to Mantaci et al. Mitsuya et al [38] considered the monotonicity of LZ77 without self-references z 77 presented a family of strings T for which z 77 (T )/z 77 (T ) ≈ 4/3 with T = [2.…”

Section: Related Worksupporting

confidence: 74%

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Sensitivity of string compressors and repetitiveness measures

Akagı¹,

Funakoshi²,

Inenaga³

2021

Preprint

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The sensitivity of a string compression algorithm C asks how much the output size C(T ) for an input string T can increase when a single character edit operation is performed on T . This notion enables one to measure the robustness of compression algorithms in terms of errors and/or dynamic changes occurring in the input string.In this paper, we analyze the worst-case multiplicative sensitivity of string compression algorithms, which is defined by max T ∈Σ n {C(T )/C(T ) : ed(T, T ) = 1}, where ed(T, T ) denotes the edit distance between T and T . In particular, for the most common versions of the Lempel-Ziv 77 compressors, we prove that the worst-case multiplicative sensitivity is only a small constant (2 or 3, depending on the version of the Lempel-Ziv 77 and the edit operation type), i.e., the size z of the Lempel-Ziv 77 factorizations can be larger by only a small constant factor. We strengthen our upper bound results by presenting matching lower bounds on the worst-case sensitivity for all these major versions of the Lempel-Ziv 77 factorizations. This contrasts with the previously known related results such that the size z 78 of the Lempel-Ziv 78 factorization can increase by a factor of Ω(n 3/4 ) [Lagarde and Perifel, 2018], and the number r of runs in the Burrows-Wheeler transform can increase by a factor of Ω(log n) [Giuliani et al., 2021] when a character is prepended to an input string of length n. We also study the worst-case sensitivity of several grammar compression algorithms including Bisection, AVL-grammar, GCIS (Grammar Compression by Induced Sorting), and CDAWG (Compact Directed Acyclic Word Graph). Further, we extend the notion of the worst-case sensitivity to string repetitiveness measures such as the smallest string attractor size γ and the substring complexity δ, and present matching upper and lower bounds of the worst-case multiplicative sensitivity for γ and δ. We also exhibit the worst-case additive sensitivity max T ∈Σ n {C(T ) − C(T ) : ed(T, T ) = 1}, which allows one to observe more details in the changes of the output sizes.

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Section: Related Worksupporting

confidence: 74%

“…|T | = n − 1). Such strings T are already known for the Lempel-Ziv 77 factorization size z when T = T [2..n] [38], or for the smallest string attractor size γ when…”

Section: Worst-case Sensitivity Of Compressors and Repetitiveness Mea...mentioning

confidence: 99%

Sensitivity of string compressors and repetitiveness measures

Akagı¹,

Funakoshi²,

Inenaga³

2021

Preprint

Self Cite

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“…In practice, the comparison of image point features is realized based on the similarities of feature points. The Hamming distance is chosen to describe the similarities between different points in this research [30][31][32]. To enhance the efficiency of initial matching, a fast search based on the K-Nearest Neighbor (KNN) algorithm is adopted in this work [33,34].…”

Section: Initial Matching and Screeningmentioning

confidence: 99%

Fast Automatic Registration of UAV Images via Bidirectional Matching

Luo,

Wei,

Jin

et al. 2023

Sensors

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Image registration plays a vital role in the mosaic process of multiple UAV (Unmanned Aerial Vehicle) images acquired from different spatial positions of the same scene. Aimed at the problem that many fast registration methods cannot provide both high speed and accuracy simultaneously for UAV visible light images, this work proposes a novel registration framework based on a popular baseline registration algorithm, ORB—the Oriented FAST (Features from Accelerated Segment Test) and Rotated BRIEF (Binary Robust Independent Elemental Features) algorithm. First, the ORB algorithm is utilized to extract image feature points fast. On this basis, two bidirectional matching strategies are presented to match obtained feature points. Then, the PROSRC (Progressive Sample Consensus) algorithm is applied to remove false matches. Finally, the experiments are carried out on UAV image pairs about different scenes including urban, road, building, farmland, and forest. Compared with the original version and other state-of-the-art registration methods, the bi-matching ORB algorithm exhibits higher accuracy and faster speed without any training or prior knowledge. Meanwhile, its complexity is quite low for on-board realization.

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“…The papers in this volume, evaluated by anonymous and expert reviewers, are related to the design of techniques and data-structures exploiting compression in order to efficiently represent families of sets (see [1]), present novel algorithms for factorization and substring compression queries (see [2]), and present a randomized communication protocol to compute the Hamming distance of compressed strings (see [3]). Moreover, two further papers in the Special Issue manage computational complexity bounds.…”

Section: Special Issuementioning

confidence: 99%