arXiv subjects

Charles Colley

Publications and source records attributed to Charles Colley.

3 recordsLinked to original sources

arXiv2025

Dominant H-Eigenvectors of Tensor Kronecker Products Do Not Decouple

We illustrate a counterexample to an open question related to the dominant H-eigenvector of a Kronecker product of tensors. For matrices and Z-eigenvectors of tensors, the dominant eigenvector of a Kronecker product decouples into a product of eigenvectors of the tensors underlying the Kronecker product. This does not occur for H-eigenvectors and indeed, the largest H-eigenvalue can exceed the product of the H-eigenvalues of the component tensors. Beyond this general counterexample, we show this decoupling does hold in the case of diagonal tensors as well as nonnegative tensors.

math.NA↗

arXiv2025

How Fast Can Graph Computations Go on Fine-grained Parallel Architectures

Large-scale graph problems are of critical and growing importance and historically parallel architectures have provided little support. In the spirit of co-design, we explore the question, How fast can graph computing go on a fine-grained architecture? We explore the possibilities of an architecture optimized for fine-grained parallelism, natural programming, and the irregularity and skew found in real-world graphs. Using two graph benchmarks, PageRank (PR) and Breadth-First Search (BFS), we evaluate a Fine-Grained Graph architecture, UpDown, to explore what performance codesign can achieve. To demonstrate programmability, we wrote five variants of these algorithms. Simulations of up to 256 nodes (524,288 lanes) and projections to 16,384 nodes (33M lanes) show the UpDown system can achieve 637K GTEPS PR and 989K GTEPS BFS on RMAT, exceeding the best prior results by 5x and 100x respectively.

cs.DC↗

arXiv2020

Dominant Z-Eigenpairs of Tensor Kronecker Products are Decoupled and Applications to Higher-Order Graph Matching

Tensor Kronecker products, the natural generalization of the matrix Kronecker product, are independently emerging in multiple research communities. Like their matrix counterpart, the tensor generalization gives structure for implicit multiplication and factorization theorems. We present a theorem that decouples the dominant eigenvectors of tensor Kronecker products, which is a rare generalization from matrix theory to tensor eigenvectors. This theorem implies low rank structure ought to be present in the iterates of tensor power methods on Kronecker products. We investigate low rank structure in the network alignment algorithm TAME, a power method heuristic. Using the low rank structure directly or via a new heuristic embedding approach, we produce new algorithms which are faster while improving or maintaining accuracy, and scale to problems that cannot be realistically handled with existing techniques.

cs.SI↗