Distributed Computing seminars

Matthias Bolten discusses the scalability of multigrid solvers for linear systems arising from discretized partial differential equations. On modern supercomputers, heterogeneous CPUs and GPUs and the widening gap between computation, network, and memory speeds complicate parallelization. Classical multigrid analysis relies on tightly coupled multiplicative components, whereas additive and asynchronous variants relax this coupling. The talk compares approaches to improving high-performance multigrid scalability, including asynchronous execution.

Vasileios Kalantzis develops iterative linear algebra algorithms that tolerate incomplete matrix-vector products in controller-worker cloud systems. Richardson and Chebyshev schemes solve linear systems using randomly available product entries, replacing missing entries with zero. For dominant eigenvectors, modified power iterations substitute zeros, previous entries, or averages of partial iterates for delayed components. The talk presents convergence results in expectation and numerical experiments on sparse matrices for both problem classes.

Evan Coleman studies how asynchronous solvers can recover convergence quality while tolerating stale data, stragglers, and variable delays. At the coordinator, Anderson acceleration connects asynchronous stationary iterations to Krylov methods with changing preconditioners and flexible GMRES. Controlled-delay experiments on high-performance computing infrastructure show that its effectiveness depends on the iteration's coupling density. At the worker, residual-weighted randomized coordinate descent includes Boltzmann weights that interpolate between uniform and greedy selection while preserving convergence guarantees. Both approaches seek better use of computation when information is inconsistent.

Paritosh Ramanan presents algorithm–hardware co-design for reliable linear algebra and optimization on resistive-memory in-memory computing systems. The distributed MELISO simulation framework supports multiple hardware models, while multilevel error correction makes noisy, low-energy devices useful for matrix-vector multiplication. Simulations report energy improvements of up to five orders of magnitude and latency reductions of up to two for high-dimensional linear algebra. A distributed primal-dual hybrid gradient solver for linear programs combines convergence analysis under device noise with simulated gains of up to two orders in latency and three in energy over GPU baselines on medium-scale problems. Preliminary randomized Kaczmarz results use online signal-to-noise estimates to select rows, comparing this strategy with offline alternatives. The talk closes with open problems in in-memory computation.

Brendan McMahan examines how AI systems can learn from high-quality information that is distributed and privacy-sensitive. He introduces principles for precise discussions of privacy and AI, then connects them to the theory and practical methods needed in real applications, including work on decentralised and privacy-preserving learning.

Robert Tarjan asks how much data-structure operations can be accelerated using multiple unsynchronised processes. The presentation examines the challenges of exploiting concurrency through joint work with Siddhartha Jayanti on efficient concurrent disjoint-set union. It includes recent approaches that remove the need for randomisation.