Layout problems on lattice graphs

Authors:
Josep Díaz;Mathew D. Penrose;Jordi Petit;María Serna
Affiliations:
Departament de Llenguatges i Sistemes Informátics, Universitat Politècnica de Catalunya, Barcelona, Spain;Department of Mathematical Sciences, University of Durham, Durham, England;Departament de Llenguatges i Sistemes Informátics, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Llenguatges i Sistemes Informátics, Universitat Politècnica de Catalunya, Barcelona, Spain
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

Citing 4
Cited 2

Optimal numberings of an N N array

SIAM Journal on Algebraic and Discrete Methods
The bisection width of grid graphs

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Linear Layouts of Generalized Hypercubes

WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
A new rounding procedure for the assignment problem with applications to dense graph arrangement problems

FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science

Linear Orderings of Random Geometric Graphs

WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs

Combinatorics, Probability and Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 the value for the constant in the mentioned theorem.