Related papers: Central Triangulation under Parallel Flip Operatio…
Given a point set $\mathcal{P}$ and a plane perfect matching $\mathcal{M}$ on $\mathcal{P}$, a flip is an operation that replaces two edges of $\mathcal{M}$ such that another plane perfect matching on $\mathcal{P}$ is obtained. Given two…
Flips of diagonals in colored triangle-free triangulations of a convex polygon are interpreted as moves between two adjacent chambers in a certain graphic hyperplane arrangement. Properties of geodesics in the associated flip graph are…
The objective here is to find the maximum polygon, in area, which can be enclosed in a given triangle, for the polygons: parallelograms, rectangles and squares. It will initially be assumed that the choices are inscribed polygons, that is…
We investigate the problem of determining if a given graph corresponds to the dual of a triangulation of a simple polygon. This is a graph recognition problem, where in our particular case we wish to recognize a graph which corresponds to…
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none…
Triangle strips have been widely used for efficient rendering. It is NP-complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few…
The problem of computing the Betweenness Centrality (BC) is important in analyzing graphs in many practical applications like social networks, biological networks, transportation networks, electrical circuits, etc. Since this problem is…
Conformal mapping is an important mathematical tool in many physical and engineering fields, especially in electrostatics, fluid mechanics, classical mechanics, and transformation optics. However in the existing textbooks and literatures,…
We present a $O(n^{\frac{3}{2}})$-time algorithm for the \emph{shortest (diagonal) flip path problem} for \emph{lattice} triangulations with $n$ points, improving over previous $O(n^2)$-time algorithms. For a large, natural class of inputs,…
The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. Recently Censor and Segal proposed…
In this survey article, we are interested on minimal triangulations of closed pl manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a…
We study flip-graphs of triangulations on topological surfaces where distance is measured by counting the number of necessary flip operations between two triangulations. We focus on surfaces of positive genus $g$ with a single boundary…
This paper describes the parallel implementation of the TRANSIMS traffic micro-simulation. The parallelization method is domain decomposition, which means that each CPU of the parallel computer is responsible for a different geographical…
Recent contrastive learning methods have shown to be effective in various tasks, learning generalizable representations invariant to data augmentation thereby leading to state of the art performances. Regarding the multifaceted nature of…
Given a triangulation of a closed topological cube, we show that (under some technical condition) there is an essentially unique tiling of a rectangular parallelepiped by cubes, indexed by the vertices of the triangulation. Moreover, i -…
We propose a parallel algorithm for local, on the fly, model checking of a fragment of CTL that is well-suited for modern, multi-core architectures. This model-checking algorithm takes bene t from a parallel state space construction…
We describe a computer algorithm that searches for substitution rules on a set of triangles, the angles of which are all integer multiples of {\pi}/n. We find new substitution rules admitting 7-fold rotational symmetry at many different…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…
Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…
The flip graph is the graph whose nodes correspond to non-isomorphic combinatorial triangulations and whose edges connect pairs of triangulations that can be obtained one from the other by flipping a single edge. In this note we show that…