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Applications of types of SATs
Arash Ahadi2013
What is SAT?
What is SAT?
What is SAT?
What is SAT Problem?
What is SAT Problem?
SAT is NP-complete
Why 3-SAT is useful?
An example (in Computational Geometry)
An important open problem
Sketch of Proof
Sketch of Proof
Sketch of Proof
Sketch of Proof
Sketch of Proof
Sketch of Proof
Types of SAT
Why do we need another types of SATs?
Answer by several examples
Sketch of Proof
Sketch of Proof
Sketch of Proof
Planar 3-SAT
Other types and examples?!!
Labeling of Graphs:Lucky labeling
Existance
Hardness
Sketch of Proof
Sketch of Proof
What about every k >1?
Main Reference
Another type
Not All Equal SAT
Labeling of Graphs:Sigma labeling
The Relationship between Lucky & Sigma
They are very different
Relationship to Chromatic Number
Complexity for 3-regular graphs
Sketch of Proof
Sketch of Proof
Complexity for every k
Minimizing the size of a Part
Minimizing the size of a Part
Minimizing the size of a Part
Minimizing the size of a Part
Minimizing the size of a Part
Conclusion
The Others
Proper Labeling Problems
A. Ahadi and A. Dehghan, Journal of Theoretical Computer Science, in appears.
Edge Labeling by Sum
Proper Labeling Problems
Edge Labeling by Product
Vertex Labeling by Product
Edge Labeling by Gap
Edge Labeling by Gap
Edge Labeling by Gap
Vertex Labeling by Gap
Vertex Labeling by Gap
Polynomial Algorithm
Fractional Coloring
Fractional Coloring
The Results (in labelings)
There are several another theorems…
Thanks
