Developer-Centric Design of Branch and Bound Algorithm

We present a C++ template for writing branch and bound algorithms that are efficient yet easy to read and understand. The approach separates the logic of an abstract methodology for dealing with large search spaces efficiently from the concrete implementation of several algorithms. We describe how we have designed and implemented an abstract branch and bound method, both in sequential and parallel version, and then used it to implement algorithms for finding k-clique, maximum clique, and listing all maximal cliques. The algorithm for finding maximum clique is the main goal, since we also have access to the code of a state-of-the-art parallel algorithm available, and we can use it as reference for comparison with the new algorithm. From the experiments on 36 input graphs of various difficulty and on up to 32 CPU threads, we show that the new algorithm is not much slower than the much more optimized reference algorithm. By developing two more algorithms on the branch and bound template, we demonstrate that the proposed abstract methodology is not only efficient but also easy to use, and can facilitate the development of closely related algorithms.