Is it impossible to use an STL map together with a struct as key?

For a thing to be usable as a key in a map, you have to be able to compare it using operator<(). You need to add such an operator to your node class:

struct Node
{
 int a;
 int b;

 bool operator<( const Node & n ) const {
   return this->a < n.a;   // for example
 }
};

Of course, what the real operator does depends on what comparison actually means for your struct.

You have to tell std::map how to compare the Node objects. By default it tries to do so by using the less than operator. But you didn't provide any less than operator for Node. The easiest solution would be to supply one.

Free function example:

bool operator<(Node const& n1, Node const& n2)
{
    return n1.a<n2.a || (n1.a==n2.a && n1.b<n2.b);
}

Note that, for any pair of node objects x,y with !(x<y) and !(y<x) the map will regard x and y as equal (same key).