Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hidden Hamiltonian Cycle Recovery via Linear Programming   We introduce the problem of hidden Hamiltonian cycle recovery, where there is
an unknown Hamiltonian cycle in an $n$-vertex complete graph that needs to be
inferred from noisy edge measurements. The measurements are independent and
distributed according to $\calP_n$ for edges in the cycle and $\calQ_n$
otherwise. This formulation is motivated by a problem in genome assembly, where
the goal is to order a set of contigs (genome subsequences) according to their
positions on the genome using long-range linking measurements between the
contigs. Computing the maximum likelihood estimate in this model reduces to a
Traveling Salesman Problem (TSP). Despite the NP-hardness of TSP, we show that
a simple linear programming (LP) relaxation, namely the fractional $2$-factor
(F2F) LP, recovers the hidden Hamiltonian cycle with high probability as $n \to
\infty$ provided that $\alpha_n - \log n \to \infty$, where $\alpha_n
\triangleq -2 \log \int \sqrt{d P_n d Q_n}$ is the R\'enyi divergence of order
$\frac{1}{2}$. This condition is information-theoretically optimal in the sense
that, under mild distributional assumptions, $\alpha_n \geq (1+o(1)) \log n$ is
necessary for any algorithm to succeed regardless of the computational cost.
  Departing from the usual proof techniques based on dual witness construction,
the analysis relies on the combinatorial characterization (in particular, the
half-integrality) of the extreme points of the F2F polytope. Represented as
bicolored multi-graphs, these extreme points are further decomposed into
simpler "blossom-type" structures for the large deviation analysis and counting
arguments. Evaluation of the algorithm on real data shows improvements over
existing approaches.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom