Related papers: Fast Isotopy Computation for T-Curves
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
The existing combinatorial methods for iso-surface computation are efficient for pure visualization purposes, but it is known that the resulting iso-surfaces can have holes, and topological problems like missing or wrong connectivity can…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
Uniform sampling from the set $\mathcal{G}(\mathbf{d})$ of graphs with a given degree-sequence $\mathbf{d} = (d_1, \dots, d_n) \in \mathbb N^n$ is a classical problem in the study of random graphs. We consider an analogue for temporal…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
Acquired 3D point cloud data, whether from active sensors directly or from stereo-matching algorithms indirectly, typically contain non-negligible noise. To address the point cloud denoising problem, we propose a fast graph-based local…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
Time-Dependent Constrained Path Optimization (TD-CPO) takes the following input: (i) time-dependent (TD) road network, (ii) source ($s$), (iii) destination ($d$), (iv) departure time ($t$) and, (v) budget ($\mathcal{B}$). In TD graph, each…
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of…
Exemplar-based inpainting is the process of reconstructing missing parts of an image by searching the remaining data for patches that fit seamlessly. The image is completed to a plausible-looking solution by repeatedly inserting the patch…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
Given a real hyperelliptic algebraic curve $X$ with non-empty real part and a real effective divisor $\mc{D}$ arising via pullback from $\mathbb{P}^1$ under the hyperelliptic structure map, we study the real inflection points of the…
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
We give a method of counting the number of curves with a given type of singularity in a suitably ample linear series on a smooth surface using punctual Hilbert schemes. The types of singulaties for which our methods suffice include the…
We consider the problem of approximate counting of triangles and longer fixed length cycles in directed graphs. For triangles, T\v{e}tek [ICALP'22] gave an algorithm that returns a $(1 \pm \eps)$-approximation in…