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CSC 250

Theory of Computation

Smith Computer Science



Lecture Notes 35: More Poly-Time Reductions in NP-C


Outline

This class we'll discuss:



More reductions












Activity [2 minutes] How would you Prove this?:
(Wait; then Click)




























Upshot:

If you find k vertices connected in the graph, then they MUST be between vertices in different clauses, which means there is a combination that could be simultaneously TRUE in each clause... making \(\Phi\) == True!































TIP:

What is the most obvious vertex-cover of a graph \(G\>)?

What is the most obvious independent-set of a graph \(G\>)?



As you make the I-Set greater... what happens to the vertex-cover?

Is there a maximum I-Set in a graph \(G\>)?

What is the relation with the vertex-cover of a graph \(G\>)?


Activity [2 minutes] How would you Prove this?:
(Wait; then Click)










Upshot:

The largest I-Set must have, as its complement, the smallest vertex-cover!










Homework


[Due for everyone]
TODO

[Optional]
TODO