Final Report Summary - TAPEASE (Theory and Practice of Advanced Search and Enumeration)
This project carries out basic research at the intersection of discrete mathematics (combinatorics and algebra) and computer science (algorithm design and analysis) with the general objective of discovering, analysing, and engineering novel advanced algebraic and combinatorial methods to represent and manipulate search spaces for NP-hard combinatorial problems and canonical polynomial-time-solvable problems that yet lack satisfactory scalability to large input sizes.
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
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