Browsing by Subject "Combinatorial algorithms"

Now showing 1 - 3 of 3

Open Access
Novel algorithms and models for scaling parallel sparse tensor and matrix factorizations
(2022-07) Abubaker, Nabil F. T.
Two important and widely-used factorization algorithms, namely CPD-ALS for sparse tensor decomposition and distributed stratiﬁed SGD for low-rank matrix factorization, suﬀer from limited scalability. In CPD-ALS, the computational load associated with a tensor/subtensor assigned to a processor is a function of the nonzero counts as well as the ﬁber counts of the tensor when the CSF stor-age is utilized. The tensor ﬁbers fragment as a result of nonzero distributions, which makes balancing the computational loads a hard problem. Two strategies are proposed to tackle the balancing problem on an existing ﬁne-grain hyper-graph model: a novel weighting scheme to cover the cost of ﬁbers in the true load as well as an augmentation to the hypergraph with ﬁber nets to encode reducing the increase in computational load. CPD-ALS also suﬀers from high latency overhead due to the high number of point-to-point messages incurred as the processor count increases. A framework is proposed to limit the number of messages to O(log2 K), for a K-processor system, exchanged in log2 K stages. A hypergraph-based method is proposed to encapsulate the communication of the new log2 K-stage algorithm. In the existing stratiﬁed SGD implementations, the volume of communication is proportional to one of the dimensions of the input matrix and prohibits the scalability. Exchanging the essential data necessary for the correctness of the SSGD algorithm as point-to-point messages is proposed to reduce the volume. This, although invaluable for reducing the band-width overhead, would increase the upper bound on the number of exchanged messages from O(K) to O(K2) rendering the algorithm latency-bound. A novel Hold-and-Combine algorithm is proposed to exchange the essential communication volume with up to O(K logK) messages. Extensive experiments on HPC systems demonstrate the importance of the proposed algorithms and models in scaling CPD-ALS and stratiﬁed SGD.
Open Access
Scaling stratified stochastic gradient descent for distributed matrix completion
(Institute of Electrical and Electronics Engineers, 2023-10-01) Abubaker, Nabil; Karsavuran, M. O.; Aykanat, Cevdet
Stratified SGD (SSGD) is the primary approach for achieving serializable parallel SGD for matrix completion. State-of-the-art parallelizations of SSGD fail to scale due to large communication overhead. During an SGD epoch, these methods send data proportional to one of the dimensions of the rating matrix. We propose a framework for scalable SSGD through significantly reducing the communication overhead via exchanging point-to-point messages utilizing the sparsity of the rating matrix. We provide formulas to represent the essential communication for correctly performing parallel SSGD and we propose a dynamic programming algorithm for efficiently computing them to establish the point-to-point message schedules. This scheme, however, significantly increases the number of messages sent by a processor per epoch from O(K) to (K2) for a K-processor system which might limit the scalability. To remedy this, we propose a Hold-and-Combine strategy to limit the upper-bound on the number of messages sent per processor to O(KlgK). We also propose a hypergraph partitioning model that correctly encapsulates reducing the communication volume. Experimental results show that the framework successfully achieves a scalable distributed SSGD through significantly reducing the communication overhead. Our code is publicly available at: github.com/nfabubaker/CESSGD
Open Access
Toolkit for automated and rapid discovery of structural variants
(Academic Press, 2017) Soylev, A.; Kockan, C.; Hormozdiari, F.; Alkan C.
Structural variations (SV) are broadly defined as genomic alterations that affect >50 bp of DNA, which are shown to have significant effect on evolution and disease. The advent of high throughput sequencing (HTS) technologies and the ability to perform whole genome sequencing (WGS), makes it feasible to study these variants in depth. However, discovery of all forms of SV using WGS has proven to be challenging as the short reads produced by the predominant HTS platforms (<200 bp for current technologies) and the fact that most genomes include large amounts of repeats make it very difficult to unambiguously map and accurately characterize such variants. Furthermore, existing tools for SV discovery are primarily developed for only a few of the SV types, which may have conflicting sequence signatures (i.e. read pairs, read depth, split reads) with other, untargeted SV classes. Here we are introduce a new framework, TARDIS, which combines multiple read signatures into a single package to characterize most SV types simultaneously, while preventing such conflicts. TARDIS also has a modular structure that makes it easy to extend for the discovery of additional forms of SV. © 2017 Elsevier Inc.