Spectral Sequencing Based on Graph Distance

Abstract

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.