  We prove that the exact crossing number of a graph can be efficiently
computed for simple graphs having bounded vertex cover. In more precise words,
Crossing Number is in FPT when parameterized by the vertex cover size. This is
a notable advance since we know only very few nontrivial examples of graph
classes with unbounded and yet efficiently computable crossing number. Our
result can be viewed as a strengthening of a previous result of Lokshtanov
[arXiv, 2015] that Optimal Linear Arrangement is in FPT when parameterized by
the vertex cover size, and we use a similar approach of reducing the problem to
a tractable instance of Integer Quadratic Programming as in Lokshtanov's paper.
