# 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} }

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

### Vertex ordering and partitioning problems for random spatial graphs

- Mathematics
- 2000

Given an ordering of the vertices of a ﬁnite graph, let the induced weight for an edge be the separation of its endpoints in the ordering. Layout problems involve choosing the ordering to minimize a…

### Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs

- Mathematics, Computer ScienceCombinatorics, Probability and Computing
- 2000

The main results are convergence theorems that can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidean TSP on random points in the unit square.

### A survey of graph layout problems

- Computer ScienceCSUR
- 2002

A complete view of the current state of the art with respect to layout problems from an algorithmic point of view is presented.

### Linear Orderings of Random Geometric Graphs

- Mathematics, Computer ScienceWG
- 1999

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.

### Approximating Layout Problems on Random Geometric Graphs

- Mathematics, Computer ScienceJ. Algorithms
- 2001

This paper proves that some of the layout problems on a family of random geometric graphs remain NP-complete even for geometric graphs, and presents two heuristics that, almost surely, turn out to be constant approximation algorithms for their layout problems.

### A Polynomial Time Algorithm for the Cutwidth of Bounded Degree Graphs with Small Treewidth

- Mathematics, Computer ScienceESA
- 2001

This work shows how to construct an algorithm that, in nO(w2d) steps, computes the cutwidth of any partial w-tree with vertices of degree bounded by a fixed constant d.

### Scheduling series-parallel task graphs to minimize peak memory

- Computer Science, MathematicsTheor. Comput. Sci.
- 2018

### CUTWIDTH OF CERTAIN CLASSES OF CIRCULANT NETWORKS

- Mathematics
- 2017

The cutwidth problem of a graph G is to embed G into a path such that the maximum number of edges crossing along any cut in the path is minimized. A circulant graph Cmk(1, k) is a graph with vertex…

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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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