  We investigate the gap between theory and practice for exact branching
algorithms. In theory, branch-and-reduce algorithms currently have the best
time complexity for numerous important problems. On the other hand, in
practice, state-of-the-art methods are based on different approaches, and the
empirical efficiency of such theoretical algorithms have seldom been
investigated probably because they are seemingly inefficient because of the
plethora of complex reduction rules. In this paper, we design a
branch-and-reduce algorithm for the vertex cover problem using the techniques
developed for theoretical algorithms and compare its practical performance with
other state-of-the-art empirical methods. The results indicate that
branch-and-reduce algorithms are actually quite practical and competitive with
other state-of-the-art approaches for several kinds of instances, thus showing
the practical impact of theoretical research on branching algorithms.
