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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
Collapsing the Hierarchy of Compressed Data Structures: S...
Dominik Kempa, Tomasz Kociumaka · 2023-08-07 · via cs.DS updates on arXiv.org

In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the compressed representation of the text. A widespread phenomenon in compressed indexing is that more powerful queries require larger indexes. For example, random access, the most basic query, can be supported in $O(δ\log\frac{n\logσ}{δ\log n})$ space (where $n$ is the text length, $σ$ is the alphabet size, and $δ$ is text's substring complexity), which is the asymptotically smallest space to represent a string, for all $n$, $σ$, and $δ$ (Kociumaka, Navarro, Prezza; IEEE Trans. Inf. Theory 2023). The other end of the hierarchy is occupied by indexes supporting the powerful suffix array (SA) queries. The currently smallest one takes $O(r\log\frac{n}{r})$ space, where $r\geqδ$ is the number of runs in the BWT of the text (Gagie, Navarro, Prezza; J. ACM 2020). We present a new compressed index that needs only $O(δ\log\frac{n\logσ}{δ\log n})$ space to support SA functionality in $O(\log^{4+ε} n)$ time. This collapses the hierarchy of compressed data structures into a single point: The space required to represent the text is simultaneously sufficient for efficient SA queries. Our result immediately improves the space complexity of dozens of algorithms, which can now be executed in optimal compressed space. In addition, we show how to construct our index in $O(δ\text{ polylog } n)$ time from the LZ77 parsing of the text. For highly repetitive texts, this is up to exponentially faster than the previously best algorithm. To obtain our results, we develop numerous techniques of independent interest, including the first $O(δ\log\frac{n\logσ}{δ\log n})$-size index for LCE queries.