LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
An Analysis of Spectral Envelope Reduction via Quadratic Assignment Problems
SIAM Journal on Matrix Analysis and Applications
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A survey of graph layout problems
ACM Computing Surveys (CSUR)
On Bipartite Drawings and the Linear Arrangement Problem
SIAM Journal on Computing
A Multilevel Algorithm for Wavefront Reduction
SIAM Journal on Scientific Computing
An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem
Journal of Global Optimization
Experiments on the minimum linear arrangement problem
Journal of Experimental Algorithmics (JEA)
Graph minimum linear arrangement by multilevel weighted edge contractions
Journal of Algorithms
Laying Out Sparse Graphs with Provably Minimum Bandwidth
INFORMS Journal on Computing
A survey of solved problems and applications on bandwidth, edgesum, and profile of graphs
Journal of Graph Theory
Multiscale approach for the network compression-friendly ordering
Journal of Discrete Algorithms
Advanced coarsening schemes for graph partitioning
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
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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.