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COMP 731 - Data Struc & Algorithms - Lecture 32 - Thursday, September 21, 2000
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Today:
o How hard is SUBSET SUM?
o Evaluations
// Basically, a lecture that introduces NP-completeness without ever
// mentioning "NP".
Talk of the running time of SUBSET SUM.
It is NOT polynomial in the length of the input.
Nobody has ever found an algorithm for this problem that is polynomial
in the length of the input.
Introduce Vertex Cover (VC).
Introduce the idea of (Turing) reductions:
A reduces to B means
B can be solved in polynomial time --> A can be solved in polynomial time
Slowly give the reduction from VC to SUBSET SUM.
Use the reduction from CLR.
Use lots of colors to make this clear.
(Forget the nonsense in the book of representing things base-4;
this is just an ordinary base-10 number.)
Argue why this works.