  Graph modification problems are typically asked as follows: is there a small
set of operations that transforms a given graph to have a certain property. The
most commonly considered operations include vertex deletion, edge deletion, and
edge addition; for the same property, one can define significantly different
versions by allowing different operations. We study a very general graph
modification problem which allows all three types of operations: given a graph
$G$ and integers $k_1$, $k_2$, and $k_3$, the \textsc{chordal editing} problem
asks whether $G$ can be transformed into a chordal graph by at most $k_1$
vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. Clearly, this
problem generalizes both \textsc{chordal vertex/edge deletion} and
\textsc{chordal completion} (also known as \textsc{minimum fill-in}). Our main
result is an algorithm for \textsc{chordal editing} in time $2^{O(k\log
k)}\cdot n^{O(1)}$, where $k:=k_1+k_2+k_3$ and $n$ is the number of vertices of
$G$. Therefore, the problem is fixed-parameter tractable parameterized by the
total number of allowed operations. Our algorithm is both more efficient and
conceptually simpler than the previously known algorithm for the special case
\textsc{chordal deletion}.
