Related papers: Central Triangulation under Parallel Flip Operatio…
Counting triangles in a graph and incident to each vertex is a fundamental and frequently considered task of graph analysis. We consider how to efficiently do this for huge graphs using massively parallel distributed-memory machines.…
Flip-graph connectedness is established here for the vertex set of the 4-dimensional cube. It is found as a consequence that this vertex set has 92 487 256 triangulations, partitioned into 247 451 symmetry classes.
Planning long-horizon robot manipulation requires making discrete decisions about which objects to interact with and continuous decisions about how to interact with them. A robot planner must select grasps, placements, and motions that are…
The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds…
The One Sided Crossing Minimization (OSCM) problem is an optimization problem in graph drawing that aims to minimize the number of edge crossings in bipartite graph layouts. It has practical applications in areas such as network…
This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…
A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge…
This paper proposes an algorithm for clipping line segment against an axis-aligned rectangular window. The conventional algorithms for line segment clipping treat the clipping boundary and/or the line segment to be clipped as line. The…
This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D…
This paper is about the geometry of flip-graphs associated to triangulations of surfaces. More precisely, we consider a topological surface with a privileged boundary curve and study the spaces of its triangulations with n vertices on the…
Let P be a point inside a convex quadrilateral ABCD. The lines from P to the vertices of the quadrilateral divide the quadrilateral into four triangles. If we locate a triangle center in each of these triangles, the four triangle centers…
The generalized method to have a parallel solution to a computational problem, is to find a way to use Divide & Conquer paradigm in order to have processors acting on its own data and therefore all can be scheduled in parallel. MapReduce is…
This thesis explores two specific topics of discrete geometry, the multitriangulations and the polytopal realizations of products, whose connection is the problem of finding polytopal realizations of a given combinatorial structure. A…
Abstract. The Set Intersection Problem (SIP) is the problem of finding a point in the intersection of convex sets. This problem is typically solved by the method of alternating projections. To accelerate the convergence, the idea of using…
The problem of path planning for automated parking is usually presented as finding a collision-free path from initial to goal positions, where three out of four parking slot edges represent obstacles. We rethink the path planning problem…
We associate strand diagrams to tilings of surfaces with marked points, generalising Scott's method for triangulations of polygons. We thus obtain a map from tilings of surfaces to permutations of the marked points on boundary components,…
The Bad Triangle Transversal (BTT) problem asks for the smallest set of edges that need to be removed from a given signed graph, so that the resulting graph does not have a bad triangle. Here, a bad triangle is a triangle with exactly one…
Ensuring constraint satisfaction is a key requirement for safety-critical systems, which include most robotic platforms. For example, constraints can be used for modeling joint position/velocity/torque limits and collision avoidance.…
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…
We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.