I have a set of points in a 2D plane. I'm searching for an algorithm that:
- Draws a continuous line passing through all the points starting from a random point.
- Optimizes for the minimum total line length in Euclidean distance.
- The line should end at the point it started but not cross any other point more than once.
In plain terms, suppose we had a paper with N dots on it. We'd take a pencil starting from a random point and try to go through all the points without lifting the pencil and conclude by reaching the point we started at.
I looked into Euclidian minimum spanning tree, but what I'm looking for is a closed loop and not a graph-tree like line. What I'd like in approximation is a Convex Hull that would go through all the points and not just form the perimeter.
Can someone direct me to the right family of algorithms?