NP-complete problems | Families of sets

Maximum coverage problem

The maximum coverage problem is a classical question in computer science, computational complexity theory, and operations research.It is a problem that is widely taught in approximation algorithms. As input you are given several sets and a number . The sets may have some elements in common. You must select at most of these sets such that the maximum number of elements are covered, i.e. the union of the selected sets has maximal size. Formally, (unweighted) Maximum Coverage Instance: A number and a collection of sets .Objective: Find a subset of sets, such that and the number of covered elements is maximized. The maximum coverage problem is NP-hard, and can be approximated within under standard assumptions. This result essentially matches the approximation ratio achieved by the generic greedy algorithm used for maximization of submodular functions with a cardinality constraint. (Wikipedia).

Video thumbnail

Maximum and Minimum

Maximum and Minimum of a set In this video, I define the maximum and minimum of a set, and show that they don't always exist. Enjoy! Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh

From playlist Real Numbers

Video thumbnail

Maximum/Minimum with Quadratics (1 of 2: Axis of symmetry)

More resources available at www.misterwootube.com

From playlist Applications of Calculus

Video thumbnail

Algebra - Minimum and Maximum (4 of 4)

Visit http://ilectureonline.com for more math and science lectures! This video is part of a four part lecture in algebra where we'll take a look at problems involved in determining maximums and minimums such as the maximum area a fence of fixed length can enclose in the shape of a square

From playlist ALGEBRA 16 - FINDING MAXIMUM AND MINIMUM VALUES

Video thumbnail

EVS Session 3 POT

Extreme Value Statistics: Peak over Threshold methods

From playlist Extreme Value Statistics

Video thumbnail

Absolute Maximum/Minimum (1 of 2: Domain restricted polynomial)

More resources available at www.misterwootube.com

From playlist Applications of Differentiation

Video thumbnail

Algebra - Minimum and Maximum (2 of 4)

Visit http://ilectureonline.com for more math and science lectures! This video is part of a four part lecture in algebra where we'll take a look at problems involved in determining maximums and minimums such as the maximum area a fence of fixed length can enclose in the shape of a square

From playlist ALGEBRA 16 - FINDING MAXIMUM AND MINIMUM VALUES

Video thumbnail

What Is The Maximum Height? (Physics Shorts)

Here is how to calculate the maximum height of a projectile, if you start at an initial height.

From playlist FULL Reviews & Problems

Video thumbnail

Absolute Maximum/Minimum Values of Multivariable Functions - Part 2 of 2

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Absolute Maximum/Minimum Values of Multivariable Functions - Part 2 of 2

From playlist All Videos - Part 6

Video thumbnail

David Tse: "How to Solve NP-hard Problems in Linear Time"

Computational Genomics Summer Institute 2017 Tutorial: "How to Solve NP-hard Problems in Linear Time" David Tse, Stanford University Institute for Pure and Applied Mathematics, UCLA July 12, 2017 For more information: http://computationalgenomics.bioinformatics.ucla.edu/

From playlist Computational Genomics Summer Institute 2017

Video thumbnail

On large time behavior of growth by birth and spread – Yoshikazu Giga – ICM2018

Partial Differential Equations Invited Lecture 10.7 On large time behavior of growth by birth and spread Yoshikazu Giga Abstract: This is essentially a survey paper on a large time behavior of solutions of some simple birth and spread models to describe growth of crystal surfaces. The mo

From playlist Partial Differential Equations

Video thumbnail

Jose Antonio Font - Inference with core-collapse supernova waveforms - IPAM at UCLA

Recorded 18 November 2021. Jose Antonio Font of the University of Valencia presents "Inference with core-collapse supernova waveforms" at IPAM's Workshop III: Source inference and parameter estimation in Gravitational Wave Astronomy. Abstract: Parameter estimation of core-collapse supernov

From playlist Workshop: Source inference and parameter estimation in Gravitational Wave Astronomy

Video thumbnail

MountainWest RubyConf 2014 - Re-thinking Regression Testing by Mario Gonzalez

Regression testing is invaluable to knowing if changes to code have broken the software. However, it always seems to be the case that no matter how many tests you have in your regression buckets, bugs continue to happily creep in undetected. As a result, you are not sure if you can trust y

From playlist MWRC 2014

Video thumbnail

Map-based visualization of RF propagation for wireless communications

Do you need to study and understand the communication link between a base-station and a mobile phone, or the ability of your transmitter to cover a certain geographic area? Many different parameters affect the quality of the link between a transmitter and a receiver, such as the position,

From playlist Designing RF front end for 5G NR

Video thumbnail

High Technology High School (Team #14694) Presentation

High Technology High School from Lincroft, New Jersey was Runner Up in MathWorks Math Modeling Challenge 2021! On April 26, 2021, finalist teams presented their solution papers via Zoom to a panel of judges. Learn more about the 2021 Challenge problem topic and the winners: https://m3chall

From playlist M3 Challenge

Video thumbnail

Yuval Filmus: Monotone Submodular Optimization over a Matroid

We consider the NP-hard problem of maximizing a monotone submodular function over a matroid constraint. Vondrak's continuous greedy algorithm achieves the best possible approximation ratio 1-1/e using continuous methods. Can the same be accomplished combinatorially? We show that this is ar

From playlist HIM Lectures 2015

Video thumbnail

Yoav Benjamini: A review of challenges in high dimensional multiple inferences

Abstract: I shall classify current approaches to multiple inferences according to goals, and discuss the basic approaches being used. I shall then highlight a few challenges that await our attention : some are simple inequalities, others arise in particular applications. Recording during

From playlist Probability and Statistics

Video thumbnail

Algebra - Minimum and Maximum (3 of 4)

Visit http://ilectureonline.com for more math and science lectures! This video is part of a four part lecture in algebra where we'll take a look at problems involved in determining maximums and minimums such as the maximum area a fence of fixed length can enclose in the shape of a square

From playlist ALGEBRA 16 - FINDING MAXIMUM AND MINIMUM VALUES

Related pages

Computational complexity theory | Submodular set function | Set cover problem | Operations research | Greedy algorithm