1. Lecture 8-9 More examples

2. Integer Programming
TSP
Knapsack VC HC
3DM
Partition
Planar 3SAT
3SAT
SAT

3. Vertex-Cover is NP-complete
Proof.

6. HC is NP-complete

9. 3DM

10. Example of 3DM
Messrs. Spinnaker, Buoy, Luff, Gybe, and Windward are yacht owners. Each has a daughter, and each has named his yacht after the daughter of one of the others.
Mr. Spinnaker’s yacht, the Iris, is named after Mr. Buoy’s daughter. Mr. Buoy’s own yacht is the Daffodil; Mr. Windward’s yacht is the Jonquil; Mr. Gybe’s, the Anthea.
Daffodil is the daughter of the owner of the yacht which is named after Mr. Luff’s daughter. Mr. Windward’s daughter is named Lalage.
Who is Jonquil’s father?

14. Trash Can ( )

15. Partition

17. S= 1 1

19. Puzzle
Answer

20. Planar 3SAT

21. Planar CNF

22. Strongly Planar CNF

23. A strongly planar CNF must be a planar CNF!!!

24. 2-3CNF

25. Planar 2-3SAT

26. Strongly Planar 2-3SAT

27. Planar 3SAT

28. Want to show