scholarly journals Computational Complexity of Fixed Points and Intersection Points

1995 ◽  
Vol 11 (2) ◽  
pp. 265-292 ◽  
Author(s):  
K.I. Ko
Keyword(s):  
Computational Complexity ◽  
Fixed Points ◽  
Intersection Points

Fast and Robust Method for Boolean Operations on Triangulated Solids Based on Signed Octree

2014 ◽  
Author(s):  
Shuai Zheng ◽  
Jun Hong ◽  
Wei Wang ◽  
Baotong Li ◽  
Xianming Gao
Keyword(s):  
Data Structure ◽  
Computational Complexity ◽  
Selection Process ◽  
Robust Method ◽  
Boolean Operations ◽  
Commercial Software ◽  
Root Node ◽  
Bounding Box ◽  
Complex Models ◽  
Intersection Points

In this paper, a fast and robust method for Boolean operations on triangulated solids is presented. It is applied to regularized Boolean operations including union, difference, and intersection. This approach is less time costing because a signed Octree and several optimizations are introduced in the algorithm. The operation starts with the minimum bounding box of the models to form the root node of the Octree, which is then continuously divided into sub-nodes, until triangles in each sub-node only have a number of triangles from both meshes, or the sub-node reaches a certain depth. After the Octree division, we run a traverse of the Octree to calculate intersection points between two meshes. This only occurs with triangles from each mesh in the very bottom sub-node of the Octree. With an in/out sign addicted to triangle’s data structure, the final facet selection process is greatly simplified. The computational complexity is highly reduced through this method with the accuracy remains to the same level. This hierarchical Octree based method enables us to do Boolean calculation on very complex models. In the end, we give some sample results and some comparisons with other algorithms and commercial software.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

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