Tree trace reconstruction using subtraces

TL;DR

This paper introduces a new proof technique for tree trace reconstruction that generalizes existing results to broader tree topologies and deletion models, using the concept of subtraces to connect with string trace algorithms.

Contribution

It provides an alternative proof for sample complexity bounds and extends the results to more general tree structures and deletion models.

Findings

Generalizes sample complexity bounds to broader tree classes

Introduces the concept of subtraces for tree reconstruction

Connects tree trace reconstruction with string trace algorithms

Abstract

Tree trace reconstruction aims to learn the binary node labels of a tree, given independent samples of the tree passed through an appropriately defined deletion channel. In recent work, Davies, R\'acz, and Rashtchian used combinatorial methods to show that $\exp(\mathcal{O}(k \log_{k} n))$ samples suffice to reconstruct a complete $k$-ary tree with $n$ nodes with high probability. We provide an alternative proof of this result, which allows us to generalize it to a broader class of tree topologies and deletion models. In our proofs, we introduce the notion of a subtrace, which enables us to connect with and generalize recent mean-based complex analytic algorithms for string trace reconstruction.