## Multilevel algorithms for linear ordering problems (2007)

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Citations: | 9 - 6 self |

### BibTeX

@MISC{Safro07multilevelalgorithms,

author = {Ilya Safro and Dorit Ron and Achi Brandt},

title = {Multilevel algorithms for linear ordering problems},

year = {2007}

}

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### Abstract

Linear ordering problems are combinatorial optimization problems which deal with the minimization of different functionals in which the graph vertices are mapped onto (1, 2,..., n). 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 running time of the algorithms enables testing very large graphs.