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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Grammar Index By Induced Suffix Sorting
Tooru Akagi, Dominik Köppl, Yuto Nakashima, Shunsuke Inenaga, Hi · 2021-05-28 · via cs.DS updates on arXiv.org

Pattern matching is the most central task for text indices. Most recent indices leverage compression techniques to make pattern matching feasible for massive but highly-compressible datasets. Within this kind of indices, we propose a new compressed text index built upon a grammar compression based on induced suffix sorting [Nunes et al., DCC'18]. We show that this grammar exhibits a locality sensitive parsing property, which allows us to specify, given a pattern $P$, certain substrings of $P$, called cores, that are similarly parsed in the text grammar whenever these occurrences are extensible to occurrences of $P$. Supported by the cores, given a pattern of length $m$, we can locate all its $occ$ occurrences in a text $T$ of length $n$ within $O(m \lg |\mathcal{S}| + occ_C \lg|\mathcal{S}| \lg n + occ)$ time, where $\mathcal{S}$ is the set of all characters and non-terminals, $occ$ is the number of occurrences, and $occ_C$ is the number of occurrences of a chosen core $C$ of $P$ in the right hand side of all production rules of the grammar of $T$. Our grammar index requires $O(g)$ words of space and can be built in $O(n)$ time using $O(g)$ working space, where $g$ is the sum of the right hand sides of all production rules. We underline the strength of our grammar index with an exhaustive practical evaluation that gives evidence that our proposed solution excels at locating long patterns in highly-repetitive texts.