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In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
This paper presents a novel and effective technique for extracting multiple ellipses from an image. The approach employs an evolutionary algorithm to mimic the way animals behave collectively assuming the overall detection process as a…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
In recent years, new regularization methods based on (deep) neural networks have shown very promising empirical performance for the numerical solution of ill-posed problems, e.g., in medical imaging and imaging science. Due to the…
Recent research on graph embedding has achieved success in various applications. Most graph embedding methods preserve the proximity in a graph into a manifold in an embedding space. We argue an important but neglected problem about this…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
Due to computational constraints, climate simulations cannot resolve a range of small-scale physical processes, which have a significant impact on the large-scale evolution of the climate system. Parameterization is an approach to capture…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…
Many geometry processing techniques require the solution of partial differential equations (PDEs) on manifolds embedded in $\mathbb{R}^2$ or $\mathbb{R}^3$, such as curves or surfaces. Such manifold PDEs often involve boundary conditions…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When cutting away a region from a solid piece of material -- such as steel, wood, ceramics, or plastic -- using a rough tool in a…
With the advent of the era of foundation models, pre-training and fine-tuning have become common paradigms. Recently, parameter-efficient fine-tuning has garnered widespread attention due to its better balance between the number of…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a…
Neural network compression empowers the effective yet unwieldy deep convolutional neural networks (CNN) to be deployed in resource-constrained scenarios. Most state-of-the-art approaches prune the model in filter-level according to the…
Robust iterative methods for solving large sparse systems of linear algebraic equations often suffer from the problem of optimizing the corresponding tuning parameters. To improve the performance of the problem of interest, specific…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…