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cs.DS updates on arXiv.org

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
Rank and Select on Degenerate Strings
Philip Bille, Inge Li Gørtz, Tord Stordalen · 2023-10-31 · via cs.DS updates on arXiv.org

A 'degenerate string' is a sequence of subsets of some alphabet; it represents any string obtainable by selecting one character from each set from left to right. Recently, Alanko et al. generalized the rank-select problem to degenerate strings, where given a character $c$ and position $i$ the goal is to find either the $i$th set containing $c$ or the number of occurrences of $c$ in the first $i$ sets [SEA 2023]. The problem has applications to pangenomics; in another work by Alanko et al. they use it as the basis for a compact representation of 'de Bruijn Graphs' that supports fast membership queries. In this paper we revisit the rank-select problem on degenerate strings, introducing a new, natural parameter and reanalyzing existing reductions to rank-select on regular strings. Plugging in standard data structures, the time bounds for queries are improved exponentially while essentially matching, or improving, the space bounds. Furthermore, we provide a lower bound on space that shows that the reductions lead to succinct data structures in a wide range of cases. Finally, we provide implementations; our most compact structure matches the space of the most compact structure of Alanko et al. while answering queries twice as fast. We also provide an implementation using modern vector processing features; it uses less than one percent more space than the most compact structure of Alanko et al. while supporting queries four to seven times faster, and has competitive query time with all the remaining structures.