Extremal optimization of graph partitioning at the percolation threshold

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performan ce of this new method, called extremal optimization (EO), is compared with simulated annealing (SA) in extensive numerical simulations. While generall y a complex (NP-hard) problem, the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near t he percolation threshold. At this threshold, the relative error of SA for l arge graphs is found to diverge relative to EO at equalized runtime. On the other hand, EO, based on the extremal dynamics of self-organized critical systems, reproduces known results about optimal partitions at this critical point quite well.