Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Parallel-Axis Theorem for an Area

Parallel-Axis Theorem for an Area

The moment of inertia is a fundamental concept in mechanical engineering that plays a significant role in designing rotationally symmetric objects such as flywheels, gears, and other mechanical systems. In this context, we will discuss the moment of inertia of a flywheel rotating about its centroidal axis and how it relates to the moment of inertia about an axis parallel to it.
For a flywheel approximated as a solid disc, consider an infinitesimal differential element with an arbitrary distance...

Area Computation by the Alternative Coordinate Method

Area Computation by the Alternative Coordinate Method

The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...

Parallel-axis Theorem

Parallel-axis Theorem

The parallel-axis theorem provides a convenient and quick method of finding the moment of inertia of an object about an axis parallel to the axis passing through its center of mass. Consider a thin rod as an example. There is a striking similarity between the process of finding the moment of inertia of a thin rod about an axis through its middle, where the center of mass lies, and about an axis through its end using the conventional method. In the conventional method, the concept of linear mass...

Vectors in 2D: Problem Solving

Vectors in 2D: Problem Solving

A plane traveling due north at 180 km/h in still air was found to be 80 km off-course after 30 minutes, deviating approximately 5 degrees east of north. This deviation means the influence of a crosswind alters the plane’s intended trajectory. The actual ground path formed a diagonal, suggesting that the aircraft’s effective ground speed was reduced to 160 km/h and directed slightly to the east due to the wind.By analyzing the displacement from the intended path, the velocity contributed by the...

Optimization Problems

Optimization Problems

Optimization problems often involve identifying maximum or minimum values under specific constraints. A well-known example is determining the longest horizontal pipe that can be moved around a right-angled corner, where a 3-meter-wide hallway meets a 2-meter-wide hallway. This scenario, common in architectural design and industrial transport, can be understood conceptually through geometric and trigonometric reasoning.To visualize the problem, consider the pipe as a straight line that touches...

Collisions in Multiple Dimensions: Problem Solving

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...

You might also read

Related Articles

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

Sort by

Same author

The chitin catabolic cascade in the marine bacterium Vibrio furnissii. Characterization of an N,N'-diacetyl-chitobiose transport system.

The Journal of biological chemistry·1996

Same author

The optimal tidal volume delivered by ventilator after pulmonary resection: its effect on cardiopulmonary hemodynamics.

Artificial organs·1996

Same author

Using titanium plate or meshplate for chest wall reconstruction: report of 6 cases and literature review.

Artificial organs·1996

Same author

Molecular cloning and expression of human Gal beta 1,3GalNAc alpha 2,3-sialytransferase (hST3Gal II).

Biochemical and biophysical research communications·1996

Same author

Aggressive polyfibromatosis: a 10 year follow-up.

The Australasian journal of dermatology·1996

Same author

The carbohydrate moiety of the bermuda grass antigen BG60. New oligosaccharides of plant origin.

The Journal of biological chemistry·1996

Same journal

Universal perceptron and DNA-like learning algorithm for binary neural networks: LSBF and PBF implementations.

IEEE transactions on neural networks·2013

Same journal

Guest editorial: special section on white box nonlinear prediction models.

IEEE transactions on neural networks·2011

Same journal

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

IEEE transactions on neural networks·2011

Same journal

Guest editorial: special section on data-based control, modeling, and optimization.

IEEE transactions on neural networks·2011

Same journal

Neural network-based multiple robot simultaneous localization and mapping.

IEEE transactions on neural networks·2011

Same journal

Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems.

IEEE transactions on neural networks·2011

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 7, 2026

Rapid Setup of Tissue Microarray and Tiled Area Imaging on the Multiplexed Ion Beam Imaging Microscope Using the Tile/SED/Array Interface

Rapid Setup of Tissue Microarray and Tiled Area Imaging on the Multiplexed Ion Beam Imaging Microscope Using the Tile/SED/Array Interface

Published on: September 15, 2023

A parallel algorithm for tiling problems.

Y Takefuji¹, Y C Lee

¹Dept. of Electr. Eng. and Appl. Phys., Case Western Reserve Univ., Cleveland, OH.

IEEE Transactions on Neural Networks

|January 1, 1990

Summary

This summary is machine-generated.

This study introduces a parallel algorithm for efficiently tiling with polyominoes. This computational geometry solution offers rapid packing on checkerboards, applicable to VLSI design and circuit board optimization.

More Related Videos

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Published on: May 8, 2015

Related Experiment Videos

Last Updated: Jul 7, 2026

Rapid Setup of Tissue Microarray and Tiled Area Imaging on the Multiplexed Ion Beam Imaging Microscope Using the Tile/SED/Array Interface

Rapid Setup of Tissue Microarray and Tiled Area Imaging on the Multiplexed Ion Beam Imaging Microscope Using the Tile/SED/Array Interface

Published on: September 15, 2023

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Published on: May 8, 2015

Area of Science:

Computational Geometry
Parallel Algorithms
Discrete Mathematics

Background:

The polyomino tiling problem involves packing shapes onto a grid.
Efficient algorithms are crucial for complex packing challenges in various industries.
Existing methods may lack the speed required for large-scale applications.

Purpose of the Study:

To present a novel parallel algorithm for solving the polyomino tiling problem.
To achieve constant time complexity for tiling operations.
To demonstrate the algorithm's applicability to practical design and packing problems.

Main Methods:

Development of a parallel algorithm utilizing lxmxn processing elements.
Analysis of time complexity, achieving O(1) for tiling operations.
Demonstration of the algorithm's performance based on the number of polyomino types (l) and checkerboard dimensions (mxn).

Main Results:

A parallel algorithm for polyomino tiling with O(1) time complexity has been developed.
The algorithm's efficiency is dependent on the number of polyomino types and checkerboard size.
Successful application demonstrated for VLSI component placement and printed circuit board design.

Conclusions:

The presented parallel algorithm offers a highly efficient solution for polyomino tiling.
This method has significant implications for optimizing component placement in VLSI and circuit board design.
The algorithm provides a versatile tool for diverse 2D and 3D packing problems.