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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
Efficiently Computing Edit Distance to Dyck Language
Barna Saha · 2013-11-12 · via cs.DS updates on arXiv.org

Given a string $σ$ over alphabet $Σ$ and a grammar $G$ defined over the same alphabet, how many minimum number of repairs: insertions, deletions and substitutions are required to map $σ$ into a valid member of $G$ ? We investigate this basic question in this paper for $Dyck(s)$. $Dyck(s)$ is a fundamental context free grammar representing the language of well-balanced parentheses with s different types of parentheses and has played a pivotal role in the development of theory of context free languages. Computing edit distance to $Dyck(s)$ significantly generalizes string edit distance problem and has numerous applications ranging from repairing semi-structured documents such as XML to memory checking, automated compiler optimization, natural language processing etc. In this paper we give the first near-linear time algorithm for edit distance computation to $Dyck(s)$ that achieves a nontrivial approximation factor of $O(\frac{1}ε\log{OPT}(\log{n})^{\frac{1}ε})$ in $O(n^{1+ε}\log{n})$ time. In fact, given there exists an algorithm for computing string edit distance on input of size $n$ in $α(n)$ time with $β(n)$-approximation factor, we can devise an algorithm for edit distance problem to $Dyck(s)$ running in $\tilde{O}(n^{1+ε}+α(n))$ and achieving an approximation factor of $O(\frac{1}εβ(n)\log{OPT})$. We show that the framework for efficiently approximating edit distance to $Dyck(s)$ can be applied to many other languages. We illustrate this by considering various memory checking languages which comprise of valid transcripts of stacks, queues, priority queues, double-ended queues etc. Therefore, any language that can be recognized by these data structures, can also be repaired efficiently by our algorithm.