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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
On Conditional Branches in Optimal Search Trees
Michael B. Baer · 2006-04-06 · via cs.DS updates on arXiv.org

Algorithms for efficiently finding optimal alphabetic decision trees -- such as the Hu-Tucker algorithm -- are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus independent of the outcome of the decision. The few algorithms without this assumption instead use one cost if the decision outcome is ``less than'' and another cost otherwise. In practice, neither assumption is accurate for software optimized for today's microprocessors. Such software generally has one cost for the more likely decision outcome and a greater cost -- often far greater -- for the less likely decision outcome. This problem and generalizations thereof are thus applicable to hard coding static decision tree instances in software, e.g., for optimizing program bottlenecks or for compiling switch statements. An O(n^3)-time O(n^2)-space dynamic programming algorithm can solve this optimal binary decision tree problem, and this approach has many generalizations that optimize for the behavior of processors with predictive branch capabilities, both static and dynamic. Solutions to this formulation are often faster in practice than ``optimal'' decision trees as formulated in the literature. Different search paradigms can sometimes yield even better performance.