Optimum Broadcasting in Complete Weighted-Vertex Graphs

2010 ◽  
pp. 489-502 ◽  
Author(s):  
Hovhannes Harutyunyan ◽  
Shahin Kamali
Keyword(s):  
Weighted Vertex

Dual-Primal Mesh Optimization for Polygonized Implicit Surfaces With Sharp Features

2002 ◽  
Vol 2 (4) ◽  
pp. 277-284 ◽  
Author(s):  
Yutaka Ohtake ◽  
Alexander G. Belyaev
Keyword(s):  
Adaptive Mesh ◽  
Implicit Surfaces ◽  
Marching Cubes ◽  
Triangle Mesh ◽  
Implicit Surface ◽  
Weighted Vertex ◽  
Visualization Toolkit ◽  
Object Oriented Approach ◽  
Speed And Accuracy ◽  
Dual Mesh

A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard Marching Cubes mesh [Lorensen, W.E., and Cline, H.E., 1987, Computer Graphics (Proceedings of SIGGRAPH ’87), 21(3), pp. 163–169] (in our experiments we use VTK Marching Cubes [Schroeder, W., Martin, K., and Lorensen, W., 1998, The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics, Prentice Hall]). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that “double dual” mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvature-weighted vertex resampling. The proposed method outperforms approaches based on the mesh evolution paradigm in speed and accuracy.

Approximating Dynamic Weighted Vertex Cover with Soft Capacities

Algorithmica ◽  
2021 ◽  
Author(s):  
Hao-Ting Wei ◽  
Wing-Kai Hon ◽  
Paul Horn ◽  
Chung-Shou Liao ◽  
Kunihiko Sadakane
Keyword(s):  
Vertex Cover ◽  
Weighted Vertex

Adaptive feasible and infeasible tabu search for weighted vertex coloring

2018 ◽  
Vol 466 ◽  
pp. 203-219 ◽  
Author(s):  
Wen Sun ◽  
Jin-Kao Hao ◽  
Xiangjing Lai ◽  
Qinghua Wu
Keyword(s):  
Tabu Search ◽  
Vertex Coloring ◽  
Weighted Vertex

scholarly journals Parameterized Analysis of Multiobjective Evolutionary Algorithms and the Weighted Vertex Cover Problem

2019 ◽  
Vol 27 (4) ◽  
pp. 559-575
Author(s):  
Mojgan Pourhassan ◽  
Feng Shi ◽  
Frank Neumann
Keyword(s):  
Evolutionary Algorithm ◽  
Complexity Analysis ◽  
Minimum Weight ◽  
Vertex Cover ◽  
Optimal Solution ◽  
Population Based ◽  
Mutation Operator ◽  
Vertex Cover Problem ◽  
Weighted Vertex ◽  
Cover Problem

Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann ( 2013 ) in the context of parameterized complexity analysis. This article extends the analysis to the weighted vertex cover problem in which integer weights are assigned to the vertices and the goal is to find a vertex cover of minimum weight. Using an alternative mutation operator introduced in Kratsch and Neumann ( 2013 ), we provide a fixed parameter evolutionary algorithm with respect to [Formula: see text], the cost of an optimal solution for the problem. Moreover, we present a multiobjective evolutionary algorithm with standard mutation operator that keeps the population size in a polynomial order by means of a proper diversity mechanism, and therefore, manages to find a 2-approximation in expected polynomial time. We also introduce a population-based evolutionary algorithm which finds a [Formula: see text]-approximation in expected time [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document