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.
- Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek (2004). Computational Homology. Springer. ISBN 0-387-40853-3.
- Afra J. Zomorodian (2005). Topology for Computing. Cambridge. ISBN 0-521-83666-2.
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