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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
Indexing and querying color sets of images
Djamal Belazzougui, Roman Kolpakov, Mathieu Raffinot · 2016-08-29 · via cs.DS updates on arXiv.org

We aim to study the set of color sets of continuous regions of an image given as a matrix of $m$ rows over $n\geq m$ columns where each element in the matrix is an integer from $[1,σ]$ named a {\em color}. The set of distinct colors in a region is called fingerprint. We aim to compute, index and query the fingerprints of all rectangular regions named rectangles. The set of all such fingerprints is denoted by ${\cal F}$. A rectangle is {\em maximal} if it is not contained in a greater rectangle with the same fingerprint. The set of all locations of maximal rectangles is denoted by $\mathcal{L}.$ We first explain how to determine all the $|\mathcal{L}|$ maximal locations with their fingerprints in expected time $O(nm^2σ)$ using a Monte Carlo algorithm (with polynomially small probability of error) or within deterministic $O(nm^2σ\log(\frac{|\mathcal{L}|}{nm^2}+2))$ time. We then show how to build a data structure which occupies $O(nm\log n+\mathcal{|L|})$ space such that a query which asks for all the maximal locations with a given fingerprint $f$ can be answered in time $O(|f|+\log\log n+k)$, where $k$ is the number of maximal locations with fingerprint $f$. If the query asks only for the presence of the fingerprint, then the space usage becomes $O(nm\log n+|{\cal F}|)$ while the query time becomes $O(|f|+\log\log n)$. We eventually consider the special case of squared regions (squares).