Experiments on the minimum linear arrangement problem

This paper deals with the Minimum Linear Arrangement problem from an experimental point of view. Using a testsuite of sparse graphs, we experimentally compare several algorithms to obtain upper and lower bounds for this problem. The algorithms considered include Successive Augmentation heuristics, Local Search heuristics and Spectral Sequencing. The testsuite is based on two random models and "real life" graphs. As a consequence of this study, two main conclusions can be drawn: On one hand, the best approximations are usually obtained using Simulated Annealing, which involves a large amount of computation time. Solutions found with Spectral Sequencing are close to the ones found with Simulated Annealing and can be obtained in significantly less time. On the other hand, we notice that there exists a big gap between the best obtained upper bounds and the best obtained lower bounds. These two facts together show that, in practice, finding lower and upper bounds for the Minimum Linear Arrangement problem is hard.