Optimal numberings of an N N array
SIAM Journal on Algebraic and Discrete Methods
On the probable performance of Heuristics for bandwidth minimization
SIAM Journal on Computing
A Spectral Algorithm for Seriation and the Consecutive Ones Problem
SIAM Journal on Computing
Finding near-optimal cuts: an empirical evaluation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
The bisection width of grid graphs
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Eigenvalues and graph bisection: An average-case analysis
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Layout problems on lattice graphs
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
DCOSS'10 Proceedings of the 6th IEEE international conference on Distributed Computing in Sensor Systems
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In random geometric graphs, vertices are randomly distributed on [0, 1]2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cut, Minimum Sum Cut, Vertex Separation and Bisection. We first prove that some of these problems remain NP-complete even for geometric graphs. Afterwards, we compute lower bounds that hold with high probability on random geometric graphs. Finally, we characterize the probabilistic behavior of the lexicographic ordering for our layout problems on the class of random geometric graphs.