12/3 CSE 202 - NP-complete
CSE 202 - Algorithms
NP Completeness
Approximations
CSE 202 - NP-complete2
Decision Problems
Instance: an input, an output, and a size.
Problem: a set of instances.
Decision Problem: Problem where each instance’s output is “T” or “F”.
“Given graph G and nodes x and y, what is the shortest
path from x to y?” is
not
a decision problem.
“Given G, x, y, and k, is there a path from x to y of length
£k?”
Usually, given an algorithm for a decision problem, one can
use it to solve the associated optimization problem.
–E.g., use binary search: “Is there a path of length £50?”,
“£25?“, “£37?“, ... .
(You know this
already.)
