Final Report Summary - TAPEASE (Theory and Practice of Advanced Search and Enumeration)
The key outcomes of the project include [1,2] a novel algebraic framework for correctness-proof-producing and error-tolerant parallel algorithms in which the state of the computation across the processors is encoded with a Reed-Solomon code, new randomized [3] and deterministic [4] algorithm designs for finding outlier-correlated pairs of observables with subquadratic scaling in the number of observables in the input, [5] algebraic methods for designing more efficient distributed algorithms in the congested clique model of distributed computation, [6,7] engineering novel algebraic algorithms for scalable motif search on graphs, [8] generalized Laplacian techniques for hard graph problems such as Hamiltonicity, [9] a probabilistic tensor framework for the design of randomized algebraic algorithms, and [10] using tensor networks on hypergraphs as a model of computation to evaluate multilinear maps.
[1] https://doi.org/10.1145/2933057.2933101
[2] https://doi.org/10.1137/1.9781611975055.16
[3] https://doi.org/10.1137/1.9781611974331.ch90
[4] https://doi.org/10.4230/LIPIcs.ESA.2016.52
[5] https://doi.org/10.1145/2767386.2767414
[6] https://doi.org/10.1137/1.9781611973754.10
[7] https://doi.org/10.4230/LIPIcs.SEA.2018.28
[8] https://doi.org/10.4230/LIPIcs.ICALP.2017.91
[9] https://doi.org/10.1137/1.9781611975482.31
[10] https://doi.org/10.4230/LIPIcs.ITCS.2019.7