In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand our understanding of this problem by giving general results in the case of arbitrary trees. Namely, we give: a reduction from the tree trace reconstruction problem to the more classical string reconstruction problem when the tree topology is known, a lower bound for learning arbitrary tree topologies, and a general algorithm for learning the topology of any tree using techniques of Nazarov and Peres (2017). We conclude by discussing why arbitrary trees require exponentially many samples under the left propagation model.

翻译：在本文中,我们考虑了从树木编辑距离模型的痕迹中重建树木的问题。Davies等人(2019年)以前的工作分析了重建有标签树木的特殊案例。在这项工作中,我们通过在任意树木方面提供一般结果,极大地扩大了对这一问题的理解。也就是说,我们给出:在已知树木结构学的情况下,将树木的痕迹重建问题从树木的痕迹重建问题减少到比较古典的线条重建问题,学习任意树木结构学的起点较低,以及使用Nazarov和Peres(2017年)技术学习任何树的地形学的一般算法。我们最后通过讨论任意树木在左侧传播模式下需要大量样品的原因。