SLIDE 1
1
NP-Complete Problems Lot’s of NP Complete Problems
- When confronted with trying to show a
problem is NP-Complete
– There are lots to chose from which to perform a reduction. – Garey and Johnson lists over 300 (and that was printed in 1979.
The big 7
- Basic core of known NP-complete
problems.
– Basis for beginner in chosing a problem for reduction – From Garey and Johnson.
The Big Daddy
- SATISFIABILITY
– INSTANCE
- A set of U boolean variables and a collection C of
boolean clauses over U
– PROBLEM
- Is there a satisfying truth assignment for C?
– The one that started it all!
The other 6
- 3-SATISFIABILITY (3-SAT)
– INSTANCE:
- Collection C = {c1,c2, …, cm } of boolean clauses on
a finite set of boolean variables U such that each ci contains exactly 3 variables.
– PROBLEM:
- Is there a truth assignment for U that satisfies all
clauses of C
The other 6
- 3-DIMENSIONAL MATCHING (3DM)
– INSTANCE:
- A set M ⊆ (W x X x Y) where W, X, Y are disjoint
sets having the same number of elements
– PROBLEM
- Does M contain a matching
– A subset M’ ⊆ M such that M’ has the same size as M and no 2 elements in M’ agree in any coordinate.