  We give two algorithms computing representative families of linear and
uniform matroids and demonstrate how to use representative families for
designing single-exponential parameterized and exact exponential time
algorithms. The applications of our approach include
  - LONGEST DIRECTED CYCLE
  - MINIMUM EQUIVALENT GRAPH (MEG)
  - Algorithms on graphs of bounded treewidth
  -k-PATH, k-TREE, and more generally, k-SUBGRAPH ISOMORPHISM, where the
k-vertex pattern graph is of constant treewidth.
