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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
Efficient Reporting of Top-k Subset Sums
Biswajit Sanyal, Subhashis Majumder, Priya Ranjan Sinha Mahapatr · 2021-05-24 · via cs.DS updates on arXiv.org

The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k best subsets of objects with the lowest (or highest) overall scores are required. Given an input set R of n real numbers and a positive integer k, our target is to generate the k best subsets of R such that the sum of their elements is minimized. Our solution methodology is based on constructing a metadata structure G for a given n. Each node of G stores a bit vector of size n from which a subset of R can be retrieved. Here it is shown that the construction of the whole graph G is not needed. To answer a query, only implicit traversal of the required portion of G on demand is sufficient, which obviously gets rid of the preprocessing step, thereby reducing the overall time and space requirement. A modified algorithm is then proposed to generate each subset incrementally, where it is shown that it is possible to do away with the explicit storage of the bit vector. This not only improves the space requirement but also improves the asymptotic time complexity. Finally, a variation of our algorithm that reports only the top-k subset sums has been compared with an existing algorithm, which shows that our algorithm performs better both in terms of time and space requirement by a constant factor.