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