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Creators/Authors contains: "Brailovskaya, Tatiana"

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  1. ; (, Geometric and Functional Analysis)
    Free, publicly-accessible full text available December 1, 2025
  2. ; (, Journal of Applied Probability)
    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, Rácz, and Rashtchian [10] used combinatorial methods to show that $$\exp({\mathrm{O}} (k \log_{k} n))$$ 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. 
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