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Characterizations of Admissible Objective Functions for Hierarchical Clustering Efficient Parameter Estimation of Truncated Boolean Product Distributions Faster Hamiltonian Monte Carlo by Learning Leapfrog Scale: a self-calibrated randomized solution An Atypical Survey of Typical-Case Heuristic Algorithms LAYERWIDTH: Analysis of a New Metric for Directed Acyclic Graphs Phase Transition of Tractability in Constraint Satisfaction and Bayesian Network Inference Creating a level playing field for all symbols in a discretization Efficient MRF Energy Minimization via Adaptive Diminishing Smoothing Dynamic Stochastic Orienteering Problems for Risk-Aware Applications Submodularity in Batch Active Learning and Survey Problems on Gaussian Random Fields Learning implicitly in reasoning in PAC-Semantics On Finding Optimal Polytrees Achieving Approximate Soft Clustering in Data Streams On finding minimal w-cutset A Complete Anytime Algorithm for Treewidth Design, Evaluation and Analysis of 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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.