Related papers: Applications of fast triangulation simplification
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
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.…
A recent result of Eden, Levi, and Ron (ECCC 2015) provides a sublinear time algorithm to estimate the number of triangles in a graph. Given an undirected graph $G$, one can query the degree of a vertex, the existence of an edge between…
We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
We revisit the algorithmic problem of finding a triangle in a graph (\textsc{Triangle Detection}), and examine its relation to other problems such as \textsc{3Sum}, \textsc{Independent Set}, and \textsc{Graph Coloring}. We obtain several…
Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
After defining convex near-polygons, a formula enumerating the number of triangulations of such configurations is derived in terms of edge-polynomials. The paper describes also a transfer-matrix approach for computing quantities related to…
The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…
We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where…
We describe a randomized algorithm that, given a set $P$ of points in the plane, computes the best location to insert a new point $p$, such that the Delaunay triangulation of $P\cup\{p\}$ has the largest possible minimum angle. The expected…
Given a set of $n$ points on a plane, in the Minimum Weight Triangulation problem, we wish to find a triangulation that minimizes the sum of Euclidean length of its edges. This incredibly challenging problem has been studied for more than…
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…
A fundamental problem in computational geometry is to compute an obstacle-avoiding Euclidean shortest path between two points in the plane. The case of this problem on polygonal obstacles is well studied. In this paper, we consider the…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
The exact complexity of geometric cuts and bisections is the longstanding open problem including even the dimension one. In this paper, we resolve this problem for dimension one (the real line) by designing an exact polynomial time…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in $R^3$, (ii) reporting intersections between query lines…