Algorithms for geometric reconstruction problems

任何曾经玩过纸笔谜题（如数独、数黑、Nonogram或Bridges）的人都解决过一个重建问题：给定物体的部分信息，根据它重建物体。我建议研究这样的重建问题，这不仅是谜题的动机，更重要的是许多医学和工业应用。 我的方法是从理论计算机科学的角度。 因此，主要的问题是：“这个重建问题能在合理的短时间内由计算机解决吗？“如果是，那么目标是找到最快的算法来做到这一点。 如果没有，那么就需要使用逻辑分析，我的目标是开发出至少在某些特殊情况下性能良好的逻辑分析。

Anyone who has ever played a pen-and-paper puzzle (such as Sudoku, Kakuro, Nonogram or Bridges) has solved a reconstruction problem: given some partial information about an object, reconstruct the object from it. I propose to study such reconstruction problems, which are motivated not only by puzzles, but more importantly by many medical and industrial applications. My approach is from a theoretical computer science point of view. Thus, the main question is: "Can this reconstruction problem be solved by a computer in reasonably short time?" If yes, then the goal is to find the fastest possible algorithm to do so. If no, then heuristics are required, and my goal is to develop heuristics that performs provably well, at least in some special cases.