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

P
Proofpoint News Feed
T
The Blog of Author Tim Ferriss
aimingoo的专栏
aimingoo的专栏
M
MIT News - Artificial intelligence
N
Netflix TechBlog - Medium
Y
Y Combinator Blog
B
Blog RSS Feed
H
Help Net Security
Blog — PlanetScale
Blog — PlanetScale
Vercel News
Vercel News
Google DeepMind News
Google DeepMind News
Microsoft Security Blog
Microsoft Security Blog
G
Google Developers Blog
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
博客园 - 司徒正美
L
LangChain Blog
IT之家
IT之家
F
Fortinet All Blogs
V
V2EX
C
Check Point Blog
The Cloudflare Blog
博客园_首页
阮一峰的网络日志
阮一峰的网络日志
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
All instantiations of the greedy algorithm for the shorte...
Maksim Nikolaev · 2021-02-11 · via cs.DS updates on arXiv.org

In the Shortest Common Superstring problem (SCS), one needs to find the shortest superstring for a set of strings. While SCS is NP-hard and MAX-SNP-hard, the Greedy Algorithm "choose two strings with the largest overlap; merge them; repeat" achieves a constant factor approximation that is known to be at most 3.5 and conjectured to be equal to 2. The Greedy Algorithm is not deterministic, so its instantiations with different tie-breaking rules may have different approximation factors. In this paper, we show that it is not the case: all factors are equal. To prove this, we show how to transform a set of strings so that all overlaps are different whereas their ratios stay roughly the same. We also reveal connections between the original version of SCS and the following one: find a~superstring minimizing the number of occurrences of a given symbol. It turns out that the latter problem is equivalent to the original one.