In computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the algorithm, averaged over all possible inputs. It is frequently contrasted with worst-case complexity which considers the maximal complexity of the algorithm over all possible inputs. There are three primary motivations for studying average-case complexity. First, although some problems may be intractable in the worst-case, the inputs which elicit this behavior may rarely occur in practice, so the average-case complexity may be a more accurate measure of an algorithm's performance. Second, average-case complexity analysis provides tools and techniques to generate hard instances of problems which can be utilized in areas such as cryptography and derandomization. Third, average-case complexity allows discriminating the most efficient algorithm in practice among algorithms of equivalent best case complexity (for instance Quicksort). Average-case analysis requires a notion of an "average" input to an algorithm, which leads to the problem of devising a probability distribution over inputs. Alternatively, a randomized algorithm can be used. The analysis of such algorithms leads to the related notion of an expected complexity. (Wikipedia).
Ex: Find the Average Cost Function and Minimize the Average Cost
This video explains how to find the average cost function and find the minimum average cost given the total cost function. Site: http://mathispower4u.com
From playlist Applications of Differentiation – Maximum/Minimum/Optimization Problems
Average Rate of Change Examples
In this video we see two examples of word problems involving the average rate of change. Remember the average rate of change formula: (f(b) - f(a))/(b-a)
From playlist Calculus
Averages and Uncertainty Calculations
This video tutorial explains how to calculate the average and uncertainty given a data set. The uncertainty is half of the range or half of the difference between the maximum and minimum values in the data set.
From playlist Statistics
Big O Notation: A Few Examples
This video is about Big O Notation: A Few Examples Time complexity is commonly estimated by counting the number of elementary operations (elementary operation = an operation that takes a fixed amount of time to preform) performed in the algorithm. Time complexity is classified by the nat
From playlist Computer Science and Software Engineering Theory with Briana
Ex 1: Cost Function Applications - Marginal Cost, Average Cost, Minimum Average Cost
This video explains how several application of the cost function including total cost, marginal cost, average cost, and minimum average cost. The total cost function is a quadratic function. Site: http://mathispower4u.com
From playlist Applications of Differentiation – Maximum/Minimum/Optimization Problems
Ex 1: Average Value of a Function
This video provides an example of how to determine the average value of a function on an interval. Search Video Library at www.mathispower4u.wordpress.com
From playlist Applications of Definite Integration
Ex 2: Cost Function Applications - Marginal Cost, Average Cost, Minimum Average Cost
This video explains how several application of the cost function including total cost, marginal cost, average cost, and minimum average cost. The total cost function is a quadratic function. Site: http://mathispower4u.com
From playlist Applications of Differentiation – Maximum/Minimum/Optimization Problems
Lower bounds for subgraph isomorphism – Benjamin Rossman – ICM2018
Mathematical Aspects of Computer Science Invited Lecture 14.3 Lower bounds for subgraph isomorphism Benjamin Rossman Abstract: We consider the problem of determining whether an Erdős–Rényi random graph contains a subgraph isomorphic to a fixed pattern, such as a clique or cycle of consta
From playlist Mathematical Aspects of Computer Science
Pierre Calka: Autour de la géométrie stochastique : polytopes aléatoires et autres modèles
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Probability and Statistics
Nexus trimester - Yitong Yin (Nanjing University)
Rectangle inequalities for data structure lower bounds Yitong Yin (Nanjing University) February 23, 2016 Abstract: The richness lemma is a classic rectangle-based technique for asymmetric communication complexity and cell-probe lower bounds. The technique was enhanced by the Patrascu-Thoru
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Truly Understanding Big O Notation: An introduction to analysing algorithm efficiency #SoME2
Understand the basics of analysing algorithms using big O notation, big Omega notation and Theta notation. Here are some related videos: - Truly Understanding Bubble Sort: https://www.youtube.com/watch?v=JVilYn7kiIc - Truly Understanding Merge Sort: https://www.youtube.com/watch?v=HpPr0t8
From playlist Summer of Math Exposition 2 videos
On the possibility of an instance-based complexity theory - Boaz Barak
Computer Science/Discrete Mathematics Seminar I Topic: On the possibility of an instance-based complexity theory. Speaker: Boaz Barak Affiliation: Harvard University Date: April 15, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
A surprising application of complex numbers in combinatorics #SoME2
An adaptation of an excellent proof from the excellent "Proofs from THE BOOK" (Aigner & Ziegler) with a more intuitive and visual approach. Music: bensound.com Made with manim community edition. 0:00 - Intro 0:29 - Refresher 1:36 - The puzzle 2:25 - The h function 4:07 - The f function
From playlist Summer of Math Exposition 2 videos
Universidad de la República, Uruguay Some Results on the Complexity of the Eigenvalue Problem In this talk we will focus on the complexity of some algorithms designed for the eigenvalue problem. In particular we will present an algorithm for the eigenvalue(eigenvector) problem which runs
From playlist Fall 2019 Symbolic-Numeric Computing Seminar
Philipp Habegger: Equidistribution of roots of unity and the Mahler measure
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 25, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Testing Correlations and Inverse Theorems - Hamed Hatami
Hamed Hatami Institute for Advanced Study/Princeton University February 23, 2010 The uniformity norms are defined in different contexts in order to distinguish the ``typical'' random functions, from the functions that contain certain structures. A typical random function has small uniform
From playlist Mathematics
Searching and Sorting Algorithms (part 4 of 4)
Introductory coverage of basic searching and sorting algorithms, as well as a rudimentary overview of Big-O algorithm analysis. Part of a larger series teaching programming at http://codeschool.org
From playlist Searching and Sorting Algorithms
Finding the Class Limits, Width, Midpoints, and Boundaries from a Frequency Table
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding the Class Limits, Width, Midpoints, and Boundaries from a Frequency Table
From playlist Statistics