Reconstructing Trees from Traces
Abstract
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. For many classes of trees, including complete trees and spiders, we provide algorithms that reconstruct the labels using only a polynomial number of traces. This exhibits a stark contrast to known results on string trace reconstruction, which require exponentially many traces, and where a central open problem is to determine whether a polynomial number of traces suffice. Our techniques combine novel combinatorial and complex analytic methods.
Keywords
Cite
@article{arxiv.1902.05101,
title = {Reconstructing Trees from Traces},
author = {Sami Davies and Miklos Z. Racz and Cyrus Rashtchian},
journal= {arXiv preprint arXiv:1902.05101},
year = {2020}
}
Comments
Major revisions in the new version including algorithm descriptions, more details in section 3.1, and several new figures