Mapping the genome: some combinatorial problems arising in molecular biology
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A spectral algorithm for envelope reduction of sparse matrices
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Relaxation and clustering in a local search framework: application to linear placement
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Butterworth Filtering and Implicit Fairing of Irregular Meshes
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Large Mesh Simplification using Processing Sequences
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Sub-sampling for efficient spectral mesh processing
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
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The construction of linear mesh layouts has found various applications, such as implicit mesh filtering and mesh streaming, where a variety of layout quality criteria, e.g., span and width, can be considered. While spectral sequencing, derived from the Fiedler vector, is one of the best-known heuristics for minimizing width, it does not perform as well as the Cuthill-Mckee (CM) scheme in terms of span. In this paper, we treat optimal mesh layout generation as a problem of preserving graph distances and propose to use the subdominant eigenvector of a kernel (affinity) matrix for sequencing. Despite the non-sparsity of the affinity operators we use, the layouts can be computed efficiently for large meshes through subsampling and eigenvector extrapolation. Our experiments show that the new sequences obtained outperform those derived from the Fiedler vector, in terms of spans, and those obtained from CM, in terms of widths and other important quality criteria. Therefore, in applications where several such quality criteria can influence algorithm performance simultaneously, e.g., mesh streaming and implicit mesh filtering, the new mesh layouts could potentially provide a better trade-off.