Flip distance between triangulations of a planar point set is APX-hard
نویسندگان
چکیده
منابع مشابه
Flip distance between triangulations of a planar point set is APX-hard
In this work we consider triangulations of point sets in the Euclidean plane, i.e., maximal straight-line crossing-free graphs on a finite set of points. Given a triangulation of a point set, an edge flip is the operation of removing one edge and adding another one, such that the resulting graph is again a triangulation. Flips are a major way of locally transforming triangular meshes. We show t...
متن کاملFlip Distance Between Two Triangulations of a Point Set is NP-complete
Given two triangulations of a convex polygon, computing the minimum number of flips required to transform one to the other is a long-standing open problem. It is not known whether the problem is in P or NP-complete. We prove that two natural generalizations of the problem are NP-complete, namely computing the minimum number of flips between two triangulations of (1) a polygon with holes; (2) a ...
متن کاملComputing the Flip Distance Between Triangulations
Let T be a triangulation of a set P of n points in the plane, and let e be an edge shared by two triangles in T such that the quadrilateral Q formed by these two triangles is convex. A flip of e is the operation of replacing e by the other diagonal of Q to obtain a new triangulation of P from T . The flip distance between two triangulations of P is the minimum number of flips needed to transfor...
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Let T be a triangulation of a simple polygon. A flip in T is the operation 7 of replacing one diagonal of T by a different one such that the resulting graph is again 8 a triangulation. The flip distance between two triangulations is the smallest number 9 of flips required to transform one triangulation into the other. For the special case of 10 convex polygons, the problem of determining the sh...
متن کاملFlip Distance between Triangulations of a Simple Polygon is NP-Complete
Let T be a triangulation of a simple polygon. A flip in T is the operation of replacing one diagonal of T by a different one such that the resulting graph is again a triangulation. The flip distance between two triangulations is the smallest number of flips required to transform one triangulation into the other. For the special case of convex polygons, the problem of determining the shortest fl...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2014
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2014.01.001