Date of Award
2020
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
Gillman, David
Area of Concentration
Computer Science
Abstract
We analyze the tree trace reconstruction problem first introduced by Davies et. al. [4]. Our two main results hinge on an algorithm for reducing trees to strings under the TED deletion channel. For trees with n non-root nodes, and a reconstruction failure probability δ, we show that it is possible to learn tree-labels with T(n,δ) samples. Further, we define leaf-aware trees and fuzzy trees, and show that their structures can be learned with O(T(n,δ)) samples. We also analyze worst-case performance of deletion channels. In the left propagation deletion channel, for all deletion probabilities q, there exist trees with n non-root nodes that cannot be distinguished with less than O((1−q)−n) samples. We prove that there does not exist such a trivial edge case for the TED deletion model.
Recommended Citation
Maranzatto, Thomas, "TREE TRACE RECONSTRUCTION: SOME RESULTS" (2020). Theses & ETDs. 5966.
https://digitalcommons.ncf.edu/theses_etds/5966