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Exploring Applications of Different SAT Types in Computational Geometry

This research article delves into various types of SAT problems, focusing on their applications in computational geometry. It discusses the importance of 3-SAT, provides examples, and explores open problems. The text highlights the need for different SAT types through examples, outlines complexity issues related to labeling graphs, and presents proofs and concepts related to lucky and sigma labeling. Furthermore, it examines complexities for different graph structures and strategies for minimizing the size of components. The article concludes with insights on proper labeling problems and references for further study.

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Exploring Applications of Different SAT Types in Computational Geometry

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Presentation Transcript

  1. Applications of types of SATs ArashAhadi 2013

  2. What is SAT?

  3. What is SAT?

  4. What is SAT?

  5. What is SAT Problem?

  6. What is SAT Problem?

  7. SAT is NP-complete

  8. Why 3-SAT is useful?

  9. An example (in Computational Geometry)

  10. An important open problem

  11. Sketch of Proof

  12. Sketch of Proof

  13. Sketch of Proof

  14. Sketch of Proof

  15. Sketch of Proof

  16. Sketch of Proof

  17. Types of SAT Why do we need another types of SATs?

  18. Answer by several examples

  19. Sketch of Proof

  20. Sketch of Proof

  21. Sketch of Proof

  22. Planar 3-SAT

  23. Other types and examples?!!

  24. Labeling of Graphs:Lucky labeling

  25. Existance

  26. Hardness

  27. Sketch of Proof

  28. Sketch of Proof

  29. What about every k >1?

  30. Main Reference

  31. Another type Not All Equal SAT

  32. Labeling of Graphs:Sigma labeling

  33. The Relationship between Lucky & Sigma

  34. They are very different

  35. Relationship to Chromatic Number

  36. Complexity for 3-regular graphs

  37. Sketch of Proof

  38. Sketch of Proof

  39. Complexity for every k

  40. Minimizing the size of a Part

  41. Minimizing the size of a Part

  42. Minimizing the size of a Part

  43. Minimizing the size of a Part

  44. Minimizing the size of a Part

  45. Conclusion

  46. The Others

  47. Proper Labeling Problems Ahadi and A. Dehghan, Journal of Theoretical Computer Science, in appears.

  48. Edge Labeling by Sum

  49. Proper Labeling Problems

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