Bibliographic Details
| Title: |
Some Fast Algorithms for Curves in Surfaces. |
| Authors: |
Lackenby, Marc1 (AUTHOR) lackenby@maths.ox.ac.uk |
| Source: |
Discrete & Computational Geometry. Jul2026, Vol. 76 Issue 1, p539-588. 50p. |
| Subjects: |
Algorithms, Intersection numbers, Topology, Geometric surfaces |
| Abstract: |
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds C 1 and C 2 in a compact orientable surface S. The surface S is presented via a triangulation or a handle structure, and the 1-manifolds are given in normal form via their normal coordinates. The running time is bounded above by a polynomial function of the number of triangles in the triangulation (or the number of handles in the handle structure), and the logarithm of the weight of C 1 and C 2 . This algorithm represents an improvement over previous work, since its running time depends polynomially on the size of the triangulation of S and it can deal with closed surfaces, unlike many earlier algorithms. Another algorithm, with similar bounds on its running time, can determine whether C 1 and C 2 are isotopic. We also present a closely related algorithm that can be used to place a standard 1-manifold into normal form. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
