Computational topology

Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular computational geometry and computational complexity theory.

A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving topological problems. For example, an open problem, called the unknotting problem, is to find a polynomial time algorithm to see if a knot is unknotted.

Some parts of algorithmic topology can be considered experimental mathematics.

A major new area of computational topology is topological data analysis.