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Decomposing matrix A into a lower matrix L and an upper matrix U, which is also known as LU decomposition, is an essential operation in numerical linear algebra. For a sparse matrix, LU decomposition often introduces more nonzero entries in…
Key-based workload partitioning is a common strategy used in parallel stream processing engines, enabling effective key-value tuple distribution over worker threads in a logical operator. While randomized hashing on the keys is capable of…
While existing algorithms may be used to solve a linear system over a general field in matrix-multiplication time, the complexity of constructing a symmetric triangular factorization (LDL) has received relatively little formal study. The…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
Lifted classical planners operate directly on first-order planning tasks to avoid the computationally demanding grounding step. However, lifted planning is typically slower, as planners must repeatedly instantiate ground structures during…
Basic Linear Algebra Subprograms (BLAS) and Linear Algebra Package (LAPACK) form basic building blocks for several High Performance Computing (HPC) applications and hence dictate performance of the HPC applications. Performance in such…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
With the advent of deep learning, many dense prediction tasks, i.e. tasks that produce pixel-level predictions, have seen significant performance improvements. The typical approach is to learn these tasks in isolation, that is, a separate…
This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents a large IO file. A task can only be executed if all input and output files fit into memory, and a file can only…
In matrix factorization, available graph side-information may not be well suited for the matrix completion problem, having edges that disagree with the latent-feature relations learnt from the incomplete data matrix. We show that removing…
Multicore architectures dominate today's processor market. Even though the number of cores and threads are pretty high and continues to grow, inherently serial algorithms do not benefit from the abundance of cores and threads. In this…
A factored Nonlinear Program (Factored-NLP) explicitly models the dependencies between a set of continuous variables and nonlinear constraints, providing an expressive formulation for relevant robotics problems such as manipulation planning…
Test-time compute scaling has emerged as a powerful paradigm for enhancing mathematical reasoning in large language models (LLMs) by allocating additional computational resources during inference. However, current methods employ uniform…
Large-scale generative models like DeepSeek-R1 and OpenAI-O1 benefit substantially from chain-of-thought (CoT) reasoning, yet pushing their performance typically requires vast data, large model sizes, and full-parameter fine-tuning. While…
Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that…
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
A novel unsupervised learning method is proposed in this paper for biclustering large-dimensional matrix-valued time series based on an entirely new latent two-way factor structure. Each block cluster is characterized by its own row and…
Data analytics over normalized databases typically requires computing and materializing expensive joins (wide-tables). Factorized query execution models execution as message passing between relations in the join graph and pushes…