Smoothed analysis of algorithms

2004 ◽  
Vol 51 (3) ◽  
pp. 385-463 ◽  
Author(s):  
Daniel A. Spielman ◽  
Shang-Hua Teng
Keyword(s):  
Analysis Of Algorithms ◽  
Smoothed Analysis

Achievements and Prospects of Smoothed Analysis of Algorithms

2005 ◽  
Vol 42 (2) ◽  
pp. 286
Author(s):  
Zhiying Yang
Keyword(s):  
Analysis Of Algorithms ◽  
Smoothed Analysis

scholarly journals The Smoothed Analysis of Algorithms

2005 ◽  
pp. 17-18 ◽  
Author(s):  
Daniel A. Spielman
Keyword(s):  
Analysis Of Algorithms ◽  
Smoothed Analysis

Smoothed Analysis of Algorithms and Heuristics

2010 ◽  
pp. 274-342 ◽  
Author(s):  
Daniel A. Spielman ◽  
Shang-Hua Teng
Keyword(s):  
Analysis Of Algorithms ◽  
Smoothed Analysis

Smoothed Analysis: Analysis of Algorithms Beyond Worst Case

2011 ◽  
Vol 53 (6) ◽  
pp. 280-286 ◽  
Author(s):  
Bodo Manthey ◽  
Heiko Röglin
Keyword(s):  
Analysis Of Algorithms ◽  
Worst Case ◽  
Smoothed Analysis

Applicability analysis of algorithms for electromechanical mode identification based on measured data

2014 ◽  
Vol 31 (3) ◽  
pp. 299
Author(s):  
Kun Men ◽  
Chao Wu ◽  
Liang Tu ◽  
Chao Lu
Keyword(s):  
Analysis Of Algorithms ◽  
Measured Data ◽  
Mode Identification

Comparison and Analysis of Algorithms Used for Detecting Slums in Satellite Images

2019 ◽  
Author(s):  
Pallavi Saindane ◽  
Gayatri Ganapathy ◽  
Neha Prabhavalkar ◽  
Nilesh Bhatia ◽  
Aishwarya Vaidya
Keyword(s):  
Satellite Images ◽  
Analysis Of Algorithms ◽  
Comparison And Analysis

Computer algorithms

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Data Structures ◽  
Analysis Of Algorithms ◽  
Shortest Paths ◽  
Minimum Cut ◽  
Network Data ◽  
Computer Algorithms ◽  
Breadth First Search ◽  
Augmenting Path ◽  
Basic Concepts ◽  
Maximum Flows

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

scholarly journals Smooth input preparation for quantum and quantum-inspired machine learning

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Zhikuan Zhao ◽  
Jack K. Fitzsimons ◽  
Patrick Rebentrost ◽  
Vedran Dunjko ◽  
Joseph F. Fitzsimons
Keyword(s):  
Machine Learning ◽  
Quantum Algorithms ◽  
Machine Learning Algorithms ◽  
Low Rank ◽  
Smoothed Analysis ◽  
Machine Learning Applications ◽  
Data Points ◽  
Input Model ◽  
The Cost ◽  
Input Perturbation

AbstractMachine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum-enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states proportional to high-dimensional data points stored in a quantum accessible memory. Even given query access to exponentially many entries stored in a database, the construction of which is considered a one-off overhead, it has been argued that the cost of preparing such amplitude-encoded states may offset any exponential quantum advantage. Here we prove using smoothed analysis that if the data analysis algorithm is robust against small entry-wise input perturbation, state preparation can always be achieved with constant queries. This criterion is typically satisfied in realistic machine learning applications, where input data is subjective to moderate noise. Our results are equally applicable to the recent seminal progress in quantum-inspired algorithms, where specially constructed databases suffice for polylogarithmic classical algorithm in low-rank cases. The consequence of our finding is that for the purpose of practical machine learning, polylogarithmic processing time is possible under a general and flexible input model with quantum algorithms or quantum-inspired classical algorithms in the low-rank cases.

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