Entwurf und Analyse anwendungsbezogener geometrischer Algorithmen

这里提出的研究是一个正在进行的项目的继续，该项目考虑几何问题的启发式方法。特别是，我们研究了形状和模式匹配以及几何优化问题的方法，例如几何对象的面积有效堆叠和布局。一方面，我们计划开发这样的方法，实现它们，并通过实验来确定它们的性能。然而，另一方面，我们研究的一个主要目标是从理论上分析这些启发式算法和已经存在的启发式算法，以便能够解释它们的性能。这种分析的一部分是对算法工作良好的现实输入的考虑和表征，尽管可能存在构建的例子，其中它们表现出低效的最坏情况性能。

The research proposed here is a continuation of an ongoing project considering heuristic methods for geometric problems. In particular, we investigate such methods for shape and pattern matching and for geometric optimization problems, such as area-efficient stacking and packing of geometric objects. On the one hand we plan to develop such methods, implement them, and determine their performance experimentally. On the other hand, however, a major objective of our research is to theoretically analyze these heuristics and already existing ones in order to be able to explain their performance. Part of this analysis is the consideration and characterization of realistic inputs for which the algorithms work well although there are possibly constructed examples where they show inefficient worst case performance.