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-ofthe-art approaches for several kinds of instances, thus showing the practical impact of theoretical research on branching algorithms.
Akiba and Iwata REF were the first to show the effectiveness of the branch-and-reduce method for solving the minimum vertex cover problem in practice for large sparse real-world graphs.
Branch-and-Reduce Exponential/FPT Algorithms in Practice: A Case Study of Vertex Cover
ArXiv
ArXiv
Computer Science Mathematics