# monotone chain

> algorithm for finding the convex hull of a set of points in the plane

**Wikidata**: [Q105123714](https://www.wikidata.org/wiki/Q105123714)  
**Source**: https://4ort.xyz/entity/monotone-chain

## Summary
The monotone chain algorithm is a computational method for finding the convex hull of a set of points in the plane, similar to the Graham scan. It is an efficient convex hull algorithm with a worst-case time complexity of O(n log n).

## Key Facts
- Aliases: Andrew's algorithm
- Based on: Graham scan
- Instance of: convex hull algorithm
- Worst-case time complexity: O(n log n)
- Sitelink count: 1
- Wikidata description: algorithm for finding the convex hull of a set of points in the plane

## FAQs
### Q: What is the monotone chain algorithm used for?
A: The monotone chain algorithm is used to compute the convex hull of a set of points in the plane, which is the smallest convex polygon that contains all the points.

### Q: How does the monotone chain algorithm compare to the Graham scan?
A: Both algorithms are used for finding the convex hull of a set of points, but the monotone chain algorithm is often considered more efficient, with a similar time complexity of O(n log n).

### Q: What is the time complexity of the monotone chain algorithm?
A: The monotone chain algorithm has a worst-case time complexity of O(n log n), making it an efficient method for convex hull computation.

## Why It Matters
The monotone chain algorithm is significant in computational geometry as it provides an efficient method for determining the convex hull of a set of points. The convex hull is a fundamental concept in geometry and has applications in various fields, including computer graphics, robotics, and data analysis. By efficiently computing the convex hull, the monotone chain algorithm helps in solving problems related to point set analysis, collision detection, and pattern recognition. Its role in computational geometry ensures that it remains a valuable tool for researchers and practitioners working with spatial data.

## Notable For
- Being an efficient alternative to the Graham scan for convex hull computation.
- Having a worst-case time complexity of O(n log n), ensuring fast performance.
- Being known by the alias Andrew's algorithm, reflecting its historical development.
- Being classified as a convex hull algorithm, aligning with its core functionality.
- Having a relatively low sitelink count, indicating its niche but important role in computational geometry.

## Body
### Overview
The monotone chain algorithm is a method for computing the convex hull of a set of points in the plane. It is closely related to the Graham scan algorithm and shares a similar time complexity of O(n log n).

### Relationships
The monotone chain algorithm is based on the Graham scan, another well-known algorithm for convex hull computation. Both algorithms are used to solve the same problem but may differ in their implementation and efficiency.

### Technical Details
The monotone chain algorithm has a worst-case time complexity of O(n log n), which is efficient for large datasets. It is also referred to by the alias Andrew's algorithm, which highlights its historical significance in computational geometry.

### Applications
The convex hull computed by the monotone chain algorithm is used in various applications, including computer graphics, robotics, and data analysis. It helps in solving problems related to point set analysis, collision detection, and pattern recognition.

### Significance
The monotone chain algorithm is notable for its efficiency and reliability in convex hull computation. Its role in computational geometry ensures that it remains a valuable tool for researchers and practitioners working with spatial data.