Lecture 2-4 More examples

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=33333333333333333333 1111111111111111111111 1 1

27. Puzzle Answer

28. Planar 3SAT

29. Planar CNF

30. Strongly Planar CNF

31. A strongly planar CNF must bea planar CNF!!!

32. 2-3CNF

33. Planar 2-3SAT

34. Strongly Planar 2-3SAT

35. Planar 3SAT

36. Want to show