平面凸码是可判定的

SIAM J. Discret. Math. Pub Date : 2022-07-13 DOI:10.1137/22m1511187

B. Bukh, R. Jeffs

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引用次数: 3

摘要

我们证明了平面上每一个可由紧集实现的凸码都允许由多边形组成的实现，同样，平面上每一个开凸码都可以由多边形的内部实现。我们给出了形成这种实现所需的顶点数量的阶乘型界限。因此，我们证明了存在一种算法来决定凸码在平面上是否允许封闭或开放的实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Planar Convex Codes are Decidable

We show that every convex code realizable by compact sets in the plane admits a realization consisting of polygons, and analogously every open convex code in the plane can be realized by interiors of polygons. We give factorial-type bounds on the number of vertices needed to form such realizations. Consequently we show that there is an algorithm to decide whether a convex code admits a closed or open realization in the plane.

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SIAM J. Discret. Math.

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