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

V
V2EX
P
Proofpoint News Feed
D
DataBreaches.Net
C
Check Point Blog
L
LangChain Blog
量子位
美团技术团队
Vercel News
Vercel News
人人都是产品经理
人人都是产品经理
N
Netflix TechBlog - Medium
V
Visual Studio Blog
Microsoft Security Blog
Microsoft Security Blog
博客园 - 【当耐特】
MongoDB | Blog
MongoDB | Blog
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
Last Week in AI
Last Week in AI
The GitHub Blog
The GitHub Blog
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
U
Unit 42
腾讯CDC
M
MIT News - Artificial intelligence
Microsoft Azure Blog
Microsoft Azure Blog
Blog — PlanetScale
Blog — PlanetScale

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
Dynamic Indexability: The Query-Update Tradeoff for One-D...
Ke Yi · 2008-11-26 · via cs.DS updates on arXiv.org

The B-tree is a fundamental secondary index structure that is widely used for answering one-dimensional range reporting queries. Given a set of $N$ keys, a range query can be answered in $O(\log_B \nm + \frac{K}{B})$ I/Os, where $B$ is the disk block size, $K$ the output size, and $M$ the size of the main memory buffer. When keys are inserted or deleted, the B-tree is updated in $O(\log_B N)$ I/Os, if we require the resulting changes to be committed to disk right away. Otherwise, the memory buffer can be used to buffer the recent updates, and changes can be written to disk in batches, which significantly lowers the amortized update cost. A systematic way of batching up updates is to use the logarithmic method, combined with fractional cascading, resulting in a dynamic B-tree that supports insertions in $O(\frac{1}{B}\log\nm)$ I/Os and queries in $O(\log\nm + \frac{K}{B})$ I/Os. Such bounds have also been matched by several known dynamic B-tree variants in the database literature. In this paper, we prove that for any dynamic one-dimensional range query index structure with query cost $O(q+\frac{K}{B})$ and amortized insertion cost $O(u/B)$, the tradeoff $q\cdot \log(u/q) = Ω(\log B)$ must hold if $q=O(\log B)$. For most reasonable values of the parameters, we have $\nm = B^{O(1)}$, in which case our query-insertion tradeoff implies that the bounds mentioned above are already optimal. Our lower bounds hold in a dynamic version of the {\em indexability model}, which is of independent interests.