Multilevel algorithms for linear ordering problems

Linear ordering problems are combinatorial optimization problems that deal with the minimization of different functionals by finding a suitable permutation of the graph vertices. These problems are widely used and studied in many practical and theoretical applications. In this paper, we present a variety of linear--time algorithms for these problems inspired by the Algebraic Multigrid approach, which is based on weighted-edge contraction. The experimental result for four such problems turned out to be better than every known result in almost all cases, while the short (linear) running time of the algorithms enables testing very large graphs.