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- W2976149974 abstract "Due to its many applications, curve simplification is a long-studied problem in computational geometry and adjacent disciplines, such as graphics, geographical information science, etc. Given a polygonal curve P with n vertices, the goal is to find another polygonal curve P' with a smaller number of vertices such that P' is sufficiently similar to P. Quality guarantees of a simplification are usually given in a local sense, bounding the distance between a shortcut and its corresponding section of the curve. In this work we aim to provide a systematic overview of curve simplification problems under global distance measures that bound the distance between P and P'. We consider six different curve distance measures: three variants of the Hausdorff distance and three variants of the Frechet distance. And we study different restrictions on the choice of vertices for P'. We provide polynomial-time algorithms for some variants of the global curve simplification problem, and show NP-hardness for other variants. Through this systematic study we observe, for the first time, some surprising patterns, and suggest directions for future research in this important area." @default.
- W2976149974 created "2019-10-03" @default.
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- W2976149974 date "2019-09-09" @default.
- W2976149974 modified "2023-09-23" @default.
- W2976149974 title "Global Curve Simplification" @default.
- W2976149974 doi "https://doi.org/10.4230/lipics.esa.2019.67" @default.
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