关于层析限制条件下平铺的一个注记
A Note on Tiling under Tomographic Constraints
摘要：
给定一个二维网格的平铺，其中有几种类型的瓦片，我们可以计算每行和每列与之相交的每种类型的瓦片的数量。这些数字被称为_projects_。我们感兴趣的是重建一个有投影的瓷砖的问题。这个问题的一些简单的变种，涉及瓷砖是1x 1或1x 2矩形，在过去已经研究过，并被证明是可解的多项式时间或NP-完全。在本说明中，我们取得了进展，对各种瓷砖重建问题的全面分类，证明了几组瓷砖的NP-完全性结果。
英文摘要：
Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling which has given projections. Some simple variants of this problem, involving tiles that are 1x1 or 1x2 rectangles, have been studied in the past, and were proved to be either solvable in polynomial time or NP-complete. In this note we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving NP-completeness results for several sets of tiles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
