Robust distributed orthogonalization based on randomized aggregation

The construction of distributed algorithms for matrix computations built on top of distributed data aggregation algorithms with randomized communication schedules is investigated. For this purpose, a new aggregation algorithm for summing or averaging distributed values, the push-flow algorithm, is developed, which achieves superior resilience properties with respect to node failures compared to existing aggregation methods. On a hypercube topology it asymptotically requires the same number of iterations as the optimal all-to-all reduction operation and it scales well with the number of nodes. Orthogonalization is studied as a prototypical matrix computation task. A new fault tolerant distributed orthogonalization method (rdmGS), which can produce accurate results even in the presence of node failures, is built on top of distributed data aggregation algorithms.