Reconstructing Trees from Traces

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Sami Davies, Miklos Z. Racz, Cyrus Rashtchian ;
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:961-978, 2019.

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.

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