  We prove algorithmic results showing that a number of natural parameterized
problems are in the restricted-space parameterized classes Para-L and FPT+XL.
The first class comprises problems solvable in f(k) n^{O(1)} time using g(k) +
O(log n)) bits of space (k is the parameter and n is the input size; f and g
are computable functions). The second class comprises problems solvable under
the same time bound, but using g(k) log n bits of space instead.
  Earlier work on these classes has focused largely on their structural aspects
and their relationships with various other classes. We complement this with
Para-L and FPT+XL algorithms for a restriction of Hitting Set, some graph
deletion problems where the target class has an infinite forbidden set
characterization, a number of problems parameterized by vertex cover number,
and Feedback Vertex Set.
