163 research outputs found

    Equivalence Classes and Conditional Hardness in Massively Parallel Computations

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    The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of classical graph problems. So far, the only way to argue lower bounds for this model is to condition on conjectures about the hardness of some specific problems, such as graph connectivity on promise graphs that are either one cycle or two cycles, usually called the one cycle vs. two cycles problem. This is unlike the traditional arguments based on conjectures about complexity classes (e.g., P ? NP), which are often more robust in the sense that refuting them would lead to groundbreaking algorithms for a whole bunch of problems. In this paper we present connections between problems and classes of problems that allow the latter type of arguments. These connections concern the class of problems solvable in a sublogarithmic amount of rounds in the MPC model, denoted by MPC(o(log N)), and some standard classes concerning space complexity, namely L and NL, and suggest conjectures that are robust in the sense that refuting them would lead to many surprisingly fast new algorithms in the MPC model. We also obtain new conditional lower bounds, and prove new reductions and equivalences between problems in the MPC model

    Approximate FPGA-based LSTMs under Computation Time Constraints

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    Recurrent Neural Networks and in particular Long Short-Term Memory (LSTM) networks have demonstrated state-of-the-art accuracy in several emerging Artificial Intelligence tasks. However, the models are becoming increasingly demanding in terms of computational and memory load. Emerging latency-sensitive applications including mobile robots and autonomous vehicles often operate under stringent computation time constraints. In this paper, we address the challenge of deploying computationally demanding LSTMs at a constrained time budget by introducing an approximate computing scheme that combines iterative low-rank compression and pruning, along with a novel FPGA-based LSTM architecture. Combined in an end-to-end framework, the approximation method's parameters are optimised and the architecture is configured to address the problem of high-performance LSTM execution in time-constrained applications. Quantitative evaluation on a real-life image captioning application indicates that the proposed methods required up to 6.5x less time to achieve the same application-level accuracy compared to a baseline method, while achieving an average of 25x higher accuracy under the same computation time constraints.Comment: Accepted at the 14th International Symposium in Applied Reconfigurable Computing (ARC) 201

    Multilevel Methods for Sparsification and Linear Arrangement Problems on Networks

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    The computation of network properties such as diameter, centrality indices, and paths on networks may become a major bottleneck in the analysis of network if the network is large. Scalable approximation algorithms, heuristics and structure preserving network sparsification methods play an important role in modern network analysis. In the first part of this thesis, we develop a robust network sparsification method that enables filtering of either, so called, long- and short-range edges or both. Edges are first ranked by their algebraic distances and then sampled. Furthermore, we also combine this method with a multilevel framework to provide a multilevel sparsification framework that can control the sparsification process at different coarse-grained resolutions. Experimental results demonstrate an effectiveness of the proposed methods without significant loss in a quality of computed network properties. In the second part of the thesis, we introduce asymmetric coarsening schemes for multilevel algorithms developed for linear arrangement problems. Effectiveness of the set of coarse variables, and the corresponding interpolation matrix is the central problem in any multigrid algorithm. We are pushing the boundaries of fast maximum weighted matching algorithms for coarsening schemes on graphs by introducing novel ideas for asymmetric coupling between coarse and fine variables of the problem
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