An Algorithm for Visibility Graph Recognition on Simple Case

2009 ◽  
Author(s):  
Hossein Morady ◽  
Gholamreza Dehghani
Keyword(s):  
Visibility Graph ◽  
Graph Recognition

scholarly journals Point Visibility Graph Recognition is NP-Hard

2016 ◽  
Vol 26 (01) ◽  
pp. 1-32 ◽  
Author(s):  
Bodhayan Roy
Keyword(s):  
Polynomial Time ◽  
Visibility Graph ◽  
Np Hard ◽  
Graph Recognition ◽  
Visibility Graphs ◽  
Point Visibility

Given a 3-SAT formula, a graph can be constructed in polynomial time such that the graph is a point visibility graph if and only if the 3-SAT formula is satisfiable. This reduction establishes that the problem of recognition of point visibility graphs is NP-hard.

COMPLEXITY ASPECTS OF VISIBILITY GRAPHS

1995 ◽  
Vol 05 (03) ◽  
pp. 289-312 ◽  
Author(s):  
YAW-LING LIN ◽  
STEVEN S. SKIENA
Keyword(s):  
Optimization Problems ◽  
Dominating Set ◽  
Vertex Cover ◽  
Independent Set ◽  
Visibility Graph ◽  
Outerplanar Graph ◽  
Maximum Independent Set ◽  
Graph Recognition ◽  
Visibility Graphs ◽  
Necessary And Sufficient

In this paper, we consider two distinct problems related to complexity aspects of the visibility graphs of simple polygons. Recognizing visibility graphs is a long-standing open problem. It is not even known whether visibility graph recognition is in NP. That visibility graph recognition is in NP would be established if we could demonstrate that any n vertex visibility graph is realized by a polygon which can be drawn on an exponentially-sized grid. This motivates a study of the area requirements for realizing visibility graphs. In this paper, we prove: • Θ(n3) area is necessary and sufficient to realize the complete visibility graph Kn. • There exist visibility graphs which require exponential area to realize. • Any maximal outerplanar graph of diameter d can be realized in O(d2 · 2d) area, which can be as small as O(n log2 n) for a balanced mop. Linear maximal outer-planar graphs can be realized in O(n8) area. The second part of this paper considers the complexity of specific optimization problems on visibility graphs. Given a polygon P, we show that finding a maximum independent set, minimum vertex cover, or maximum dominating set in the visibility graph of P are all NP-complete. Further we show that for polygons P1 and P2, the problem of testing if they have isomorphic visibility graphs is isomorphism-complete. These problems remain hard when given the visibility graphs as input.

Visibility Graph Analysis of Particle Size Distribution During Flocculation for Water Treatment

2021 ◽  
Vol 232 (3) ◽  
Author(s):  
Kamila Jessie Sammarro Silva ◽  
Larissa Lopes Lima ◽  
Gustavo Santos Nunes ◽  
Lyda Patricia Sabogal-Paz
Keyword(s):  
Particle Size ◽  
Water Treatment ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Visibility Graph ◽  
Graph Analysis ◽  
Visibility Graph Analysis
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