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• W2307197129 abstract "We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertices in the plane, the problem Minimum Perimeter Polygon (MPP) asks for a (not necessarily simply connected) polygon with shortest possible boundary length. Even though the closely related problem of finding a minimum cycle cover is polynomially solvable by matching techniques, we prove how the topological structure of a polygon leads to NP-hardness of the MPP. On the positive side, we show how to achieve a constant-factor approximation. When trying to solve MPP instances to provable optimality by means of integer programming, an additional difficulty compared to the TSP is the fact that only a subset of subtour constraints is valid, depending not on combinatorics, but on geometry. We overcome this difficulty by establishing and exploiting additional geometric properties. This allows us to reliably solve a wide range of benchmark instances with up to 600 vertices within reasonable time on a standard machine. We also show that using a natural geometry-based sparsification yields results that are on average within 0.5 % of the optimum." @default.
• W2307197129 created "2016-06-24" @default.
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• W2307197129 date "2016-01-01" @default.
• W2307197129 modified "2023-10-14" @default.
• W2307197129 title "Computing Nonsimple Polygons of Minimum Perimeter" @default.
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• W2307197129 doi "https://doi.org/10.1007/978-3-319-38851-9_10" @default.
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