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The document reviews concepts related to NP-completeness, including reductions between problems. It provides examples of reducing the directed Hamiltonian cycle problem to the undirected version. It also reduces 3-SAT to the clique problem by transforming a Boolean formula to a graph, then further reduces clique to vertex cover. Hundreds of problems have been shown to be NP-complete through relatively simple reductions like these that leverage previous results.

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CS 332: Algorithms NP Completeness Continued: Reductions
Review: P and NP ,[object Object],[object Object],[object Object]
Review: P and NP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: NP-Complete ,[object Object],[object Object],[object Object],[object Object]
Review: NP-Complete ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Proving Problems NP-Complete ,[object Object],[object Object]
Review: Directed  Undirected Ham. Cycle ,[object Object],[object Object],[object Object],[object Object]
Review: Directed  Undirected Ham. Cycle ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Hamiltonian Cycle  TSP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Hamiltonian Cycle  TSP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The SAT Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Conjunctive Normal Form ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The 3-CNF Problem ,[object Object],[object Object],[object Object],[object Object]
3-CNF  Clique ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
3-CNF  Clique ,[object Object],[object Object]
3-CNF  Clique ,[object Object],[object Object],[object Object],[object Object],[object Object]
3-CNF  Clique ,[object Object],[object Object],[object Object],[object Object],[object Object]
Clique  Vertex Cover ,[object Object],[object Object],[object Object],[object Object]
Clique  Vertex Cover ,[object Object],[object Object],[object Object],[object Object],[object Object]
Clique  Vertex Cover ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Clique  Vertex Cover ,[object Object],[object Object],[object Object],[object Object],[object Object]
General Comments ,[object Object],[object Object],[object Object]
Other NP-Complete Problems ,[object Object],[object Object],[object Object],[object Object],[object Object]
The End

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lecture 30

  • 1. CS 332: Algorithms NP Completeness Continued: Reductions
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