Related papers: Distance and intersection number in the curve grap…

The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…

We use the $p$-Laplacian with large $p$-values in order to approximate geodesic distances to features on surfaces. This differs from Fayolle and Belyaev's (2018) [1] computational results using the $p$-Laplacian for the distance-to-surface…

The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…

We initiate the study of diameter computation in geometric intersection graphs from the fine-grained complexity perspective. A geometric intersection graph is a graph whose vertices correspond to some shapes in $d$-dimensional Euclidean…

We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…

The strong geodetic problem on a graph $G$ is to determine a smallest set of vertices such that by fixing one shortest path between each pair of its vertices, all vertices of $G$ are covered. To do this as efficiently as possible, strong…

We propose a second version of the van der Waals density functional (vdW-DF2) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient…

We present an approach of computing the intersection curve $\mathcal{C}$ of two rational parametric surface $\S_1(u,s)$ and $\S_2(v,t)$, one being projectable and hence can easily be implicitized. Plugging the parametric surface to the…

We complement our study of 2-connectivity in directed graphs, by considering the computation of the following 2-vertex-connectivity relations: We say that two vertices v and w are 2-vertex-connected if there are two internally…

For a compact surface $S$ with constant negative curvature $-\kappa$ (for some $\kappa>0$) and genus $g\geq2$, we show that the tails of the distribution of $i(\alpha,\beta)/l(\alpha)l(\beta)$ (where $i(\alpha,\beta)$ is the intersection…

We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…

We introduce a new dynamic data structure for maintaining the strongly connected components (SCCs) of a directed graph (digraph) under edge deletions, so as to answer a rich repertoire of connectivity queries. Our main technical…

Motivated by applications from computer vision to bioinformatics, the field of shape analysis deals with problems where one wants to analyze geometric objects, such as curves, while ignoring actions that preserve their shape, such as…

We show that the action of the mapping class group on the space of closed curves of a closed surface effectively tracks the corresponding action on Teichm\"uller space in the following sense: for all but quantitatively few mapping classes,…

We develop a framework for incorporating edge-dependent vertex weights (EDVWs) into the hypergraph minimum s-t cut problem. These weights are able to reflect different importance of vertices within a hyperedge, thus leading to better…

The paper focuses on synthesizing optimal contact curves that can be used to ensure a rolling constraint between two bodies in relative motion. We show that geodesic based contact curves generated on both the contacting surfaces are…

Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity…

In this article we deal with the problems of finding the disimplicial arcs of a digraph and recognizing some interesting graph classes defined by their existence. A diclique of a digraph is a pair $V \to W$ of sets of vertices such that $v…

Nonlinear systems and interaction forces are pervasive in many scientific fields, such as nanoscale metrology and materials science, but their accurate identification is challenging due to their complex behaviour and inaccessibility of…

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…