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Any generic closed curve in the plane can be transformed into a simple closed curve by a finite sequence of local transformations called homotopy moves. We prove that simplifying a planar closed curve with n self-crossings requires Theta(n^{3/2}) homotopy moves in the worst case. Our algorithm improves the best previous upper bound O(n^2), which is already implicit in the...

if and only if f is flat foldable. Therefore, it
is also NP-hard to decide whether a polyhedron is weakly simple.
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Hugo A. Akitaya , Greg Aloupis, **Jeff** **Erickson**, and Csaba D. T?th ... .
Marshall Bern and Barry Hayes . The complexity of flat origami . In Proc. 7th ACM-SIAM Sympos. on Discrete Algorithms , pages 175 - 183 , 1996 .
Hsien-Chih Chang , **Jeff** **Erickson** , and Chao Xu . Detecting

A topological quadrilateral mesh \(Q\) of a connected surface in \(\mathbb {R}^3\) can be extended to a topological hexahedral mesh of the interior domain \(\varOmega \) if and only if \(Q\) has an even number of quadrilaterals and no odd cycle in \(Q\) bounds a surface inside \(\varOmega \). Moreover, if such a mesh exists, the required number of hexahedra is within a constant...

By **Jeff** **Erickson**, Published on 12/18/13

A simple path or cycle in a triangulated surface is normal if it intersects any triangle in a finite set of arcs, each crossing from one edge of the triangle to another. A normal curve is a finite set of disjoint normal paths and normal cycles. We describe an algorithm to “trace” a normal curve in \(O(\min \{ X, n^2\log X \})\) time, where \(n\) is the complexity of the surface...

]. See http://www.cs.uiuc.edu/ jeffe/pubs/schema.html for the most recent version of this paper.
**Jeff** **Erickson** was partially supported by a Sloan Fellowship, NSF CAREER Award CCR-0093348, and NSF
ITR Grant