惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

Martin Fowler
Martin Fowler
Jina AI
Jina AI
J
Java Code Geeks
Microsoft Security Blog
Microsoft Security Blog
Recent Announcements
Recent Announcements
I
InfoQ
L
LangChain Blog
The Cloudflare Blog
IT之家
IT之家
博客园 - 叶小钗
Apple Machine Learning Research
Apple Machine Learning Research
B
Blog
A
About on SuperTechFans
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
Last Week in AI
Last Week in AI
Blog — PlanetScale
Blog — PlanetScale
罗磊的独立博客
云风的 BLOG
云风的 BLOG
Microsoft Azure Blog
Microsoft Azure Blog
Engineering at Meta
Engineering at Meta
F
Fortinet All Blogs
博客园 - 聂微东
美团技术团队
博客园_首页

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
USSR is in P/poly
Nikhil Balaji, Samir Datta · 2023-10-30 · via cs.DS updates on arXiv.org

The Sum of Square Roots (SSR) problem is the following computational problem: Given positive integers $a_1, \dots, a_k$, and signs $δ_1, \dots, δ_k \in \{-1, 1\}$, check if $\sum_{i=1}^k δ_i \sqrt{a_i} > 0$. The problem is known to have a polynomial time algorithm on the real RAM model of computation, however no sub-exponential time algorithm is known in the bit or Turing model of computation. The precise computational complexity of SSR has been a notorious open problem \cite{ggj} over the last four decades. The problem is known to admit an upper bound in the third level of the \emph{Counting Hierarchy}, i.e., $\CHtwo$ and no non-trivial lower bounds are known. Even when the input numbers are \emph{small}, i.e., given in \emph{unary}, no better complexity bound was known prior to our work. In this paper, we show that the unary variant (USSR) of the sum of square roots problem is considerably easier by giving a $P/poly$ upper bound.