Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near-Optimal Average-Case Approximate Trace Reconstruction from Few
  Traces   In the standard trace reconstruction problem, the goal is to \emph{exactly}
reconstruct an unknown source string $\mathsf{x} \in \{0,1\}^n$ from
independent "traces", which are copies of $\mathsf{x}$ that have been corrupted
by a $\delta$-deletion channel which independently deletes each bit of
$\mathsf{x}$ with probability $\delta$ and concatenates the surviving bits. We
study the \emph{approximate} trace reconstruction problem, in which the goal is
only to obtain a high-accuracy approximation of $\mathsf{x}$ rather than an
exact reconstruction.
  We give an efficient algorithm, and a near-matching lower bound, for
approximate reconstruction of a random source string $\mathsf{x} \in \{0,1\}^n$
from few traces. Our main algorithmic result is a polynomial-time algorithm
with the following property: for any deletion rate $0 < \delta < 1$ (which may
depend on $n$), for almost every source string $\mathsf{x} \in \{0,1\}^n$,
given any number $M \leq \Theta(1/\delta)$ of traces from
$\mathrm{Del}_\delta(\mathsf{x})$, the algorithm constructs a hypothesis string
$\widehat{\mathsf{x}}$ that has edit distance at most $n \cdot (\delta
M)^{\Omega(M)}$ from $\mathsf{x}$. We also prove a near-matching
information-theoretic lower bound showing that given $M \leq \Theta(1/\delta)$
traces from $\mathrm{Del}_\delta(\mathsf{x})$ for a random $n$-bit string
$\mathsf{x}$, the smallest possible expected edit distance that any algorithm
can achieve, regardless of its running time, is $n \cdot (\delta M)^{O(M)}$.

10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol