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Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs  (Make Corrections)  
Josep Diaz, Mathew D. Penrose, Jordi Petit, Maria Serna



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Abstract: This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. Specifically, we consider the following problems: Minimum Linear Arrangement, Cutwidth, Sum Cut, Vertex Separation, Edge Bisection and Vertex Bisection. For full square lattices, we give optimal layouts for the problems still open. For arbitrary lattice graphs, we present best possible bounds disregarding a constant... (Update)

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BibTeX entry:   (Update)

@misc{ diaz-convergence,
  author = "Josep Diaz and Mathew D. Penrose and Jordi Petit and Maria Serna",
  title = "Convergence Theorems for Some Layout Measures on Random Lattice and Random
    Geometric Graphs",
  url = "citeseer.ist.psu.edu/716914.html" }
Citations (may not include all citations):
147   A Course in Probability Theory (context) - Chung - 1974
86   A framework for solving VLSI graph layout problems - Bhatt, Leighton - 1984
61   The shortest path through many points (context) - Beardwood, Halton et al. - 1959
39   Optimal linear ordering (context) - Adolphson, Hu - 1973
24   Cluster analysis for hypertext systems (context) - Botafogo - 1993
16   Single machine job sequencing with precedence constraints (context) - Adolphson - 1977
16   Path optimization for graph partitioning problems - Berry, Goldberg - 1999
7   Compressions and isoperimetric inequalities (context) - Bollobas, Leader - 1991
7   Layout problems on lattice graphs - D'iaz, Penrose et al. - 1999
5   Random geometric problems - D'iaz, Petit et al.
1   Linear orderings of random geometric graphs - D'iaz, Penrose et al. - 1999

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