Tristan Konolige | Searcharxiv

arXiv2020

Multigrid for Bundle Adjustment

Bundle adjustment is an important global optimization step in many structure from motion pipelines. Performance is dependent on the speed of the linear solver used to compute steps towards the optimum. For large problems, the current state of the art scales superlinearly with the number of cameras in the problem. We investigate the conditioning of global bundle adjustment problems as the number of images increases in different regimes and fundamental consequences in terms of superlinear scaling of the current state of the art methods. We present an unsmoothed aggregation multigrid preconditioner that accurately represents the global modes that underlie poor scaling of existing methods and demonstrate solves of up to 13 times faster than the state of the art on large, challenging problem sets.

cs.CV↗

arXiv2018

A Parallel Solver for Graph Laplacians

Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as problem sizes increase and single core speeds stagnate, parallelism is essential to solve such problems quickly. We present an unsmoothed aggregation multigrid method for solving graph Laplacians in a distributed memory setting. We introduce new parallel aggregation and low degree elimination algorithms targeted specifically at irregular degree graphs. These algorithms are expressed in terms of sparse matrix-vector products using generalized sum and product operations. This formulation is amenable to linear algebra using arbitrary distributions and allows us to operate on a 2D sparse matrix distribution, which is necessary for parallel scalability. Our solver outperforms the natural parallel extension of the current state of the art in an algorithmic comparison. We demonstrate scalability to 576 processes and graphs with up to 1.7 billion edges.

cs.DC↗