Lecture 2-4 More examples

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

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.

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

Vertex-Cover is NP-complete Proof.

HC is NP-complete

3DM

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?

Trash Can ( )

Partition

Subsum

S=33333333333333333333 1111111111111111111111 1 1

Puzzle Answer

Planar 3SAT

Planar CNF

Strongly Planar CNF

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

2-3CNF

Planar 2-3SAT

Strongly Planar 2-3SAT

Planar 3SAT

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