1. Lecture 2-4 More examples

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

3. Vertex Cover
Given a graph G=(V,E), find a minimum subset C of vertices such that every edge is incident to a vertex in C.

4. Decision Version
Given a graph G=(V,E) and positive integer k < |V|, is there a vertex cover C of size at most k?.

5. Vertex-Cover is NP-complete
Proof.

9. HC is NP-complete

14. 3DM

15. 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?

19. Trash Can ( )

20. Partition

21. Subsum

25. S= 1 1

27. Puzzle
Answer

28. Planar 3SAT

29. Planar CNF

30. Strongly Planar CNF

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

32. 2-3CNF

33. Planar 2-3SAT

34. Strongly Planar 2-3SAT

35. Planar 3SAT

36. Want to show