Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

38
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
38
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

355
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
355
Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

425
Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
425
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

59
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
59
Decision Making: P-value Method01:09

Decision Making: P-value Method

5.2K
The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim  is also stated. These statements can act as null and alternative hypotheses:  a null hypothesis would be a neutral statement while the alternative hypothesis can...
5.2K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

84
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
84

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A nearly optimal randomized algorithm for explorable heap selection.

Mathematical programming·2025
Same journal

A better-than-1.6-approximation for prize-collecting TSP.

Mathematical programming·2026
Same journal

A <math><mrow><mfrac><mn>4</mn> <mn>3</mn></mfrac></mrow></math> -approximation for the maximum leaf spanning arborescence problem in DAGs.

Mathematical programming·2026
Same journal

An FPTAS for Connectivity Interdiction.

Mathematical programming·2026
Same journal

A first order method for linear programming parameterized by circuit imbalance.

Mathematical programming·2026
Same journal

Tight lower bounds for block-structured integer programs.

Mathematical programming·2026
Same journal

Accelerated first-order optimization under nonlinear constraints.

Mathematical programming·2026
See all related articles

Related Experiment Video

Updated: May 24, 2025

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules
10:58

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules

Published on: July 25, 2013

17.0K

From approximate to exact integer programming.

Daniel Dadush1, Friedrich Eisenbrand2, Thomas Rothvoss3

  • 1Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands.

Mathematical Programming
|March 3, 2025
PubMed
Summary
This summary is machine-generated.

New methods leverage approximate integer programming to efficiently solve exact integer programming problems. This breakthrough offers faster algorithms for complex problems like knapsack and subset-sum.

Keywords:
Convex geometryInteger programmingLattices

More Related Videos

Author Spotlight: Optimization of Airflow Velocities in Battery Cooling Systems for Enhanced Thermal Performance and Reduced Energy Consumption
10:36

Author Spotlight: Optimization of Airflow Velocities in Battery Cooling Systems for Enhanced Thermal Performance and Reduced Energy Consumption

Published on: November 3, 2023

1.4K
Measuring Delay Discounting in Humans Using an Adjusting Amount Task
07:47

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

15.3K

Related Experiment Videos

Last Updated: May 24, 2025

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules
10:58

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules

Published on: July 25, 2013

17.0K
Author Spotlight: Optimization of Airflow Velocities in Battery Cooling Systems for Enhanced Thermal Performance and Reduced Energy Consumption
10:36

Author Spotlight: Optimization of Airflow Velocities in Battery Cooling Systems for Enhanced Thermal Performance and Reduced Energy Consumption

Published on: November 3, 2023

1.4K
Measuring Delay Discounting in Humans Using an Adjusting Amount Task
07:47

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

15.3K

Area of Science:

  • Computational Mathematics
  • Optimization Theory
  • Computer Science

Background:

  • Exact integer programming is computationally challenging.
  • Existing methods for exact integer programming are complex and time-consuming.
  • Approximate integer programming offers a faster alternative but lacks direct application to exact problems.

Purpose of the Study:

  • To develop efficient methods for exact integer programming based on approximate integer programming.
  • To achieve novel complexity results for solving integer programming problems.
  • To improve the efficiency of solving specific problems like knapsack and subset-sum.

Main Methods:

  • A cutting-plane technique iteratively reduces the volume of the feasible set.
  • Approximate integer programming is used to determine cutting planes.
  • A new asymmetric approximate Carathéodory theorem is introduced.
  • Integer programming problems in equation-standard form are reduced to multiple approximate problems.

Main Results:

  • An integer point can be found in time when component remainders are provided.
  • A general integer programming algorithm with time complexity is presented, matching the best known bound.
  • Knapsack and subset-sum problems with polynomial variable range are solved in time , improving upon previous bounds.

Conclusions:

  • The developed methods provide significant improvements in the complexity of solving integer programming problems.
  • The new algorithms offer practical advantages for problems like knapsack and subset-sum.
  • The research introduces novel algorithmic techniques and theoretical results in optimization.