Seyed Ali Mohammadi | Searcharxiv

arXiv2026

More Efficient Parallel $(Δ+1)$-Edge Coloring

This paper gives two parallel algorithms for $Δ+1$ edge coloring, where $Δ$ denotes the maximum degree of any vertex. The first is a deterministic parallel algorithm with $\tilde{O}(Δ^3)$ span and $\tilde{O}(m Δ^3)$ work. Our second algorithm and our main result is a more efficient randomized algorithm, achieving $\tilde{O}(Δ^2)$ span and $\tilde{O}(m Δ^2 )$ work both with high probability. These bounds substantially improve over the recent deterministic parallel algorithm of Elkin and Khuzman, which has $\tilde{O}(Δ^4)$ span and $\tilde{O}(m Δ^5)$ work. Our deterministic algorithm thus represents a $\tilde{O}(Δ)$ improvement on span and $\tilde{O}(Δ^2)$ on work compared to their algorithm, and our randomized algorithm improves the span and work by $\tilde{O}(Δ^2)$ and $\tilde{O}(Δ^3)$ factors, respectively. Moreover, our improvements do not come at the expense of larger logarithmic factors.

cs.DS↗

arXiv2026

When AI Bends Metal: AI-Assisted Optimization of Design Parameters in Sheet Metal Forming

Numerical simulations have revolutionized the industrial design process by reducing prototyping costs, design iterations, and enabling product engineers to explore the design space more efficiently. However, the growing scale of simulations demands substantial expert knowledge, computational resources, and time. A key challenge is identifying input parameters that yield optimal results, as iterative simulations are costly and can have a large environmental impact. This paper presents an AI-assisted workflow that reduces expert involvement in parameter optimization through the use of Bayesian optimization. Furthermore, we present an active learning variant of the approach, assisting the expert if desired. A deep learning model provides an initial parameter estimate, from which the optimization cycle iteratively refines the design until a termination condition (e.g.,energy budget or iteration limit) is met. We demonstrate our approach, based on a sheet metal forming process, and show how it enables us to accelerate the exploration of the design space while reducing the need for expert involvement.

cs.AI↗