TL;DR
This paper introduces a polynomial-time algorithm for simplifying triangulations relative to a curve by combining flips and Dehn twists, improving efficiency in topological surface analysis.
Contribution
The paper presents a novel algorithm that efficiently simplifies triangulations using a combination of flips and Dehn twists, with proven polynomial time complexity.
Findings
Algorithm operates in polynomial time
Effective simplification of triangulations relative to a curve
Potential applications in computational topology
Abstract
We give a new algorithm to simplify a given triangulation with respect to a given curve. The simplification uses flips together with powers of Dehn twists in order to complete in polynomial time in the bit-size of the curve.
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