Branch and reduce exponential/FPT algorithms in practice: A case study of vertex cover
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 has 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.
Theor. Comput. Sci.