Related papers: Approximate Trace Reconstruction
In the (deletion-channel) trace reconstruction problem, there is an unknown $n$-bit source string $x$. An algorithm is given access to independent traces of $x$, where a trace is formed by deleting each bit of~$x$ independently with…
In the trace reconstruction problem, one observes the output of passing a binary string $s \in \{0,1\}^n$ through a deletion channel $T$ times and wishes to recover $s$ from the resulting $T$ "traces." Most of the literature has focused on…
Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a query point and receives a noisy version of its distance to the target. This problem arises naturally in…
In the \emph{trace reconstruction problem}, an unknown source string $x \in \{0,1\}^n$ is sent through a probabilistic \emph{deletion channel} which independently deletes each bit with probability $\delta$ and concatenates the surviving…
Several recent works have considered the \emph{trace reconstruction problem}, in which an unknown source string $x\in\{0,1\}^n$ is transmitted through a probabilistic channel which may randomly delete coordinates or insert random bits,…
Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each…
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…
Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…
In the trace reconstruction problem, an unknown bit string ${\bf x}\in\{0,1 \}^n$ is sent through a deletion channel where each bit is deleted independently with some probability $q\in(0,1)$, yielding a contracted string $\widetilde{\bf…
We present a near-linear time algorithm that approximates the edit distance between two strings within a polylogarithmic factor; specifically, for strings of length n and every fixed epsilon>0, it can compute a (log n)^O(1/epsilon)…
In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand…
The {\em insertion-deletion channel} takes as input a binary string $x \in\{0, 1\}^n$, and outputs a string $\widetilde{x}$ where some of the bits have been deleted and others inserted independently at random. In the {\em trace…
Quartet Reconstruction, the task of recovering a phylogenetic tree from smaller trees on four species called \textit{quartets}, is a well-studied problem in theoretical computer science with far-reaching connections to statistics, graph…
Given a pair of strings, the problems of computing their Longest Common Subsequence and Edit Distance have been extensively studied for decades. For exact algorithms, LCS and Edit Distance (with character insertions and deletions) are…
We study the trace reconstruction problem for spider graphs. Let $n$ be the number of nodes of a spider and $d$ be the length of each leg, and suppose that we are given independent traces of the spider from a deletion channel in which each…
The coded trace reconstruction problem asks to construct a code $C\subset \{0,1\}^n$ such that any $x\in C$ is recoverable from independent outputs ("traces") of $x$ from a binary deletion channel (BDC). We present binary codes of rate…
Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that…
A \emph{trace} of a sequence is generated by deleting each bit of the sequence independently with a fixed probability. The well-studied \emph{trace reconstruction} problem asks how many traces are required to reconstruct an unknown binary…
The edit distance between two strings is defined as the smallest number of insertions, deletions, and substitutions that need to be made to transform one of the strings to another one. Approximating edit distance in subquadratic time is…
In the trace reconstruction problem, an unknown bit string $x \in \{0,1\}^n$ is observed through the deletion channel, which deletes each bit of $x$ with some constant probability $q$, yielding a contracted string $\widetilde{x}$. How many…