Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Efficient Distance Approximation for Graph Properties   A distance-approximation algorithm for a graph property $\mathcal{P}$ in the
adjacency-matrix model is given an approximation parameter $\epsilon \in (0,1)$
and query access to the adjacency matrix of a graph $G=(V,E)$. It is required
to output an estimate of the \emph{distance} between $G$ and the closest graph
$G'=(V,E')$ that satisfies $\mathcal{P}$, where the distance between graphs is
the size of the symmetric difference between their edge sets, normalized by
$|V|^2$. In this work we introduce property covers, as a framework for using
distance-approximation algorithms for "simple" properties to design
distance-approximation. Applying this framework we present
distance-approximation algorithms with $poly(1/\epsilon)$ query complexity for
induced $P_3$-freeness, induced $P_4$-freeness, and Chordality. For induced
$C_4$-freeness our algorithm has query complexity $exp(poly(1/\epsilon))$.
These complexities essentially match the corresponding known results for
testing these properties and provide an exponential improvement on previously
known results.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg