arXiv subjects

Liana Fong

Publications and source records attributed to Liana Fong.

4 recordsLinked to original sources

arXiv2023

"Sliced" Subwindow Search: a Sublinear-complexity Solution to the Maximum Rectangle Problem

Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow search, spans many computational domains. Yet, the problem has not been solved without demanding computational resources at least linearly proportional to the size of the matrix. In this work, we present a new approach to the problem which achieves sublinear time and memory complexities by interpolating between a small amount of equidistant sections of the matrix. Applied to natural images, our solution outperforms the state-of-the-art by achieving an 11x increase in speed and memory efficiency at 99% comparative accuracy. In general, our solution outperforms existing solutions when matrices are sufficiently large and a marginal decrease in accuracy is acceptable, such as in many problems involving natural images. As such, it is well-suited for real-time application and in a variety of computationally hard instances of the maximum rectangle problem.

cs.DS↗

arXiv2018

Matrix Factorization on GPUs with Memory Optimization and Approximate Computing

Matrix factorization (MF) discovers latent features from observations, which has shown great promises in the fields of collaborative filtering, data compression, feature extraction, word embedding, etc. While many problem-specific optimization techniques have been proposed, alternating least square (ALS) remains popular due to its general applicability e.g. easy to handle positive-unlabeled inputs, fast convergence and parallelization capability. Current MF implementations are either optimized for a single machine or with a need of a large computer cluster but still are insufficient. This is because a single machine provides limited compute power for large-scale data while multiple machines suffer from the network communication bottleneck. To address the aforementioned challenge, accelerating ALS on graphics processing units (GPUs) is a promising direction. We propose the novel approach in enhancing the MF efficiency via both memory optimization and approximate computing. The former exploits GPU memory hierarchy to increase data reuse, while the later reduces unnecessary computing without hurting the convergence of learning algorithms. Extensive experiments on large-scale datasets show that our solution not only outperforms the competing CPU solutions by a large margin but also has a 2x-4x performance gain compared to the state-of-the-art GPU solutions. Our implementations are open-sourced and publicly available.

cs.DC↗

arXiv2016

Analysis and Modeling of Social Influence in High Performance Computing Workloads

Social influence among users (e.g., collaboration on a project) creates bursty behavior in the underlying high performance computing (HPC) workloads. Using representative HPC and cluster workload logs, this paper identifies, analyzes, and quantifies the level of social influence across HPC users. We show the existence of a social graph that is characterized by a pattern of dominant users and followers. This pattern also follows a power-law distribution, which is consistent with those observed in mainstream social networks. Given its potential impact on HPC workloads prediction and scheduling, we propose a fast-converging, computationally-efficient online learning algorithm for identifying social groups. Extensive evaluation shows that our online algorithm can (1) quickly identify the social relationships by using a small portion of incoming jobs and (2) can efficiently track group evolution over time.

cs.DC↗

arXiv2016

Faster and Cheaper: Parallelizing Large-Scale Matrix Factorization on GPUs

Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity for accelerating MF much further when appropriately exploiting the GPU architectural characteristics. This paper presents cuMF, a CUDA-based matrix factorization library that implements memory-optimized alternate least square (ALS) method to solve very large-scale MF. CuMF uses a variety set of techniques to maximize the performance on either single or multiple GPUs. These techniques include smart access of sparse data leveraging GPU memory hierarchy, using data parallelism in conjunction with model parallelism, minimizing the communication overhead between computing units, and utilizing a novel topology-aware parallel reduction scheme. With only a single machine with four Nvidia GPU cards, cuMF can be 6-10 times as fast, and 33-100 times as cost-efficient, compared with the state-of-art distributed CPU solutions. Moreover, this cuMF can solve the largest matrix factorization problem ever reported yet in current literature, while maintaining impressively good performance.

cs.DC↗