# Layout Problems on Lattice Graphs

@inproceedings{Daz1999LayoutPO,
title={Layout Problems on Lattice Graphs},
author={Josep D{\'i}az and Mathew D. Penrose and Jordi Petit and Maria J. Serna},
booktitle={COCOON},
year={1999}
}
• Published in COCOON 26 July 1999
• Mathematics
This work deals with bounds on the cost of layout problems for lattice graphs and random lattice graphs. Our main result in this paper is a convergence theorem for the optimal cost of the Minimum Linear Arrangement problem and the Minimum Sum Cut problem, for the case where the underlying graph is obtained through a subcritical site percolation process. This result can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidian TSP. Finally we estimate empirically…
9 Citations

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It is proved that some of these layout problems on random geometric graphs remain NP-complete even for geometric graphs, and the probabilistic behavior of the lexicographic ordering for these problems on the class ofrandom geometric graphs is characterized.

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