We investigate a fundamental vertex-deletion problem called (Induced)
Subgraph Hitting: given a graph G and a set F of forbidden
graphs, the goal is to compute a minimum-sized set S of vertices of G such
that G−S does not contain any graph in F as an (induced)
subgraph. This is a generic problem that encompasses many well-known problems
that were extensively studied on their own, particularly (but not only) from
the perspectives of both approximation and parameterization. We focus on the
design of efficient approximation schemes, i.e., with running time
f(ε,F)⋅nO(1), which are also of significant
interest to both communities. Technically, our main contribution is a
linear-time approximation-preserving reduction from (Induced) Subgraph Hitting
on any graph class G of bounded expansion to the same problem on
bounded degree graphs within G. This yields a novel algorithmic
technique to design (efficient) approximation schemes for the problem on very
broad graph classes, well beyond the state-of-the-art. Specifically, applying
this reduction, we derive approximation schemes with (almost) linear running
time for the problem on any graph classes that have strongly sublinear
separators and many important classes of geometric intersection graphs (such as
fat-object graphs, pseudo-disk graphs, etc.). Our proofs introduce novel
concepts and combinatorial observations that may be of independent interest
(and, which we believe, will find other uses) for studies of approximation
algorithms, parameterized complexity, sparse graph classes, and geometric
intersection graphs. As a byproduct, we also obtain the first robust algorithm
for k-Subgraph Isomorphism on intersection graphs of fat objects and
pseudo-disks, with running time f(k)⋅nlogn+O(m).Comment: 60 pages, abstract shortened to fulfill the length limi