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

freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
P
Proofpoint News Feed
宝玉的分享
宝玉的分享
人人都是产品经理
人人都是产品经理
博客园_首页
爱范儿
爱范儿
博客园 - 叶小钗
aimingoo的专栏
aimingoo的专栏
S
SegmentFault 最新的问题
MyScale Blog
MyScale Blog
阮一峰的网络日志
阮一峰的网络日志
IT之家
IT之家
Microsoft Security Blog
Microsoft Security Blog
Blog — PlanetScale
Blog — PlanetScale
博客园 - 【当耐特】
Y
Y Combinator Blog
量子位
博客园 - 三生石上(FineUI控件)
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
T
The Blog of Author Tim Ferriss
月光博客
月光博客
有赞技术团队
有赞技术团队
Apple Machine Learning Research
Apple Machine Learning Research
A
About on SuperTechFans

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
Multiple Source Replacement Path Problem
Manoj Gupta, Rahul Jain, Nitiksha Modi · 2020-05-19 · via cs.DS updates on arXiv.org

One of the classical line of work in graph algorithms has been the Replacement Path Problem: given a graph $G$, $s$ and $t$, find shortest paths from $s$ to $t$ avoiding each edge $e$ on the shortest path from $s$ to $t$. These paths are called replacement paths in literature. For an undirected and unweighted graph, (Malik, Mittal, and Gupta, Operation Research Letters, 1989) and (Hershberger and Suri, FOCS 2001) designed an algorithm that solves the replacement path problem in $\tilde O(m+n)$ time. It is natural to ask whether we can generalize the replacement path problem: {\em can we find all replacement paths from a source $s$ to all vertices in $G$?} This problem is called the Single Source Replacement Path Problem. Recently (Chechik and Cohen, SODA 2019) designed a randomized combinatorial algorithm that solves the Single Source Replacement Path Problem in $\tilde O(m\sqrt n\ + n^2)$ time. One of the questions left unanswered by their work is the case when there are many sources, not one. When there are $n$ sources, the combinatorial algorithm of (Bernstein and Karger, STOC 2009) can be used to find all pair replacement path in $\tilde O(mn + n^3)$ time. However, there is no result known for any general $σ$. Thus, the problem we study is defined as follows: given a set of $σ$ sources, we want to find the replacement path from these sources to all vertices in $G$. We give a randomized combinatorial algorithm for this problem that takes $\tilde O(m\sqrt{n σ} +\ σn^2)$ time. This result generalizes both results known for this problem. Our algorithm is much different and arguably simpler than (Chechik and Cohen, SODA 2019). Like them, we show a matching conditional lower bound using the Boolean Matrix Multiplication conjecture.