CS2
Week 5: Algorithm
analysis, searching,
sorting
13
NP-Complete and NP-Hard
Problems
nThe third category of problem (NP problems) can be solved in polynomial time but only
assuming an unbounded number of processors. This means
there is no polynomial time algorithm yet
developed for these problems that would work on a single processor
- but no one can prove that such an algorithm may not be possible.
nNP problems are recognised because they can all be
reduced to a common base problem called
the satisfiability problem. The reason NP problems are studied is because a large number of
practical problems have been shown to be NP-complete or NP-hard (NP-complete have a yes/no
answer whereas NP-hard problems have a more
complex output).
nThe attempt to make computers ‘intelligent’ has hit the
NP barrier. Most activities that we do
naturally, like walking, talking, recognising objects, people and handwriting, etc, when specified to a
computer become NP-complete search
problems. Therefore much work has gone
into developing algorithms that, while still exponential in theory, perform well in practice. The human brain is an excellent
example of a computer that can solve NP
problems efficiently.