Numerous microarchitectural optimizations unlocked tremendous processing power for
deep neural networks that in turn fueled the AI revolution. With the exhaustion of such …

We consider the distributed Cholesky factorization on homogeneous nodes. Inspired by
recent progress on asymptotic lower bounds on the total communication volume required to …

Chips with hundreds to thousands of cores require scalable networks-on-chip (NoCs).
Customization of the NoC topology is necessary to reach the diverse design goals of …

In this paper, we consider two fundamental symmetric kernels in linear algebra: the
Cholesky factorization and the symmetric rank-k update (SYRK), with the classical three …

Multilinear algebra kernel performance on modern massively-parallel systems is determined
mainly by data movement. However, deriving data movement-optimal distributed schedules …

Direct solvers for dense systems of linear equations commonly use partial pivoting to ensure
numerical stability. However, pivoting can introduce significant performance overheads …

LU factorization is a key approach for solving large, dense systems of linear equations.
Partial row pivoting is commonly used to ensure numerical stability; however, the data …

Higher-order graph neural networks (HOGNNs) are an important class of GNN models that
harness polyadic relations between vertices beyond plain edges. They have been used to …

Data movements between different levels of the memory hierarchy (I/O-transitions, or simply
I/O s) are a critical performance bottleneck in modern computing. Therefore it is a problem of …

Communication lower bounds have long been established for matrix multiplication
algorithms. However, most methods of asymptotic analysis have either ignored constant …