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Complexity of the Operations Research Theory tasks can be often diminished in cases that do not require finding the exact solution. For example, forecasting two-dimensional hierarchical time series leads us to the transportation problem…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
In parallel iterative applications, computational efficiency is essential for addressing large problems. Load imbalance is one of the major performance degradation factors of parallel applications. Therefore, distributing, cleverly, and as…
In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…
Continuum Approximation (CA) is an efficient and parsimonious technique for modeling complex logistics problems. In this paper,we review recent studies that develop CA models for transportation, distribution and logistics problems with the…
Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate…
Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…
We propose a general method to analytically solve transport equations during a cosmic phase transition without making approximations based on the assumption that any transport coefficient is large. Using the MSSM as an example we derive the…
A dominant cost for query evaluation in modern massively distributed systems is the number of communication rounds. For this reason, there is a growing interest in single-round multiway join algorithms where data is first reshuffled over…
In robotics, diffusion models can capture multi-modal trajectories from demonstrations, making them a transformative approach in imitation learning. However, achieving optimal performance following this regiment requires a large-scale…
This paper describes the parallel implementation of the TRANSIMS traffic micro-simulation. The parallelization method is domain decomposition, which means that each CPU of the parallel computer is responsible for a different geographical…
We combine several recent advancements to solve $(1+\varepsilon)$-transshipment and $(1+\varepsilon)$-maximum flow with a parallel algorithm with $\tilde{O}(1/\varepsilon)$ depth and $\tilde{O}(m/\varepsilon)$ work. We achieve this by…
This paper proposes a parallel numerical algorithm to simulate the flow and the transport in a discrete fracture network taking into account the mass exchanges with the surrounding matrix. The discretization of the Darcy fluxes is based on…
We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework…
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…
In this Doctoral Dissertation we propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special (multilevel) type. We propose different…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
Data and pipeline parallelism are key strategies for scaling neural network training across distributed devices, but their high communication cost necessitates co-located computing clusters with fast interconnects, limiting their…
To overcome the communication bottlenecks observed in state-of-the-art parallel time-dependent flow solvers at extreme scales, an asynchronous computing approach that relaxes communication and synchronization at a mathematical level was…
The Progressive-X algorithm, Prog-X in short, is proposed for geometric multi-model fitting. The method interleaves sampling and consolidation of the current data interpretation via repetitive hypothesis proposal, fast rejection, and…