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Topic: On NP Completeness and Intractability
Replies: 90   Last Post: Nov 1, 2005 8:08 PM

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Michael J. Hennebry

Posts: 132
Registered: 12/11/04
Re: On NP Completeness and Intractability
Posted: Oct 25, 2005 4:12 PM
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nimmi_srivastav@yahoo.com wrote:
> 1) All the literature pertaining to intractability that I have seen
> refers to the Turing's Halting Problem. What are other common examples
> of intractable problems?
> 2) In somewhat layman terms, what exactly is the difference between
> NP-Hard and NP-Complete?
> 3) If a polynomial time algorithm is discovered for a hitherto NP-Hard
> problem, does that have any implication for the P=NP question?
> [I already know that if a polynomial time algorithm is discovered for a
> hitherto NP-Complete problem, then P=NP]
> 4) When we refer to NP, without any qualifiers, does it imply NP-Hard?


The Halting problem is undecidable.
The means that there is no algorithm that will solve it.

The P of decision problem classes P, NP, and co-NP
refers to polynomial time.

A decision problem, e.g., does integer X divide integer Y,
is in P iff it can be solved in polynomial time.

A decision problem, e.g. is X composite, is in NP iff for
instances where the answer is yes the answer can be verified
in polynomial time with a lucky guess, e.g a factor of X.

A decision problem, e.g. is X prime, is in co-NP iff
its opposite, e.g. is X composite or 1, is in NP.

NP-complete and NP-hard are usually used as adjectives, e.g.
SAT is NP-complete.
The class of NP-complete problems is sometimes called NPC.
I've never seen NPH.

A problem is NP-complete iff any problem in NP can be converted
to it in polynomial time.
That is the mechanism by which finding a polynomial algorithm
for NPC would allow solving all of NP and co-NP in polynomial time.

An NP-hard problem is at least as hard as every problem in NP.
Another poster said that an NP-hard problem need not be a decision
problem.
An NP-hard decision problem need not be in NP, but it must be
decidable.

There are other classifications of decision problems.
E.g. PSPACE is the class of decision problems whose
solution requires a only polynomial amount of memory.
It includes decidable problems that are in neither NP
nor co-NP.



Date Subject Author
10/25/05
Read On NP Completeness and Intractability
nimmi_srivastav@yahoo.com
10/25/05
Read Re: On NP Completeness and Intractability
Dr. David Kirkby
10/25/05
Read Re: On NP Completeness and Intractability
ianparker2@gmail.com
10/25/05
Read Re: On NP Completeness and Intractability
Pubkeybreaker
10/25/05
Read Re: On NP Completeness and Intractability
osmium
10/25/05
Read Re: On NP Completeness and Intractability
Pubkeybreaker
10/25/05
Read Re: On NP Completeness and Intractability
Willem
10/25/05
Read Re: On NP Completeness and Intractability
Bryan Olson
10/25/05
Read Re: On NP Completeness and Intractability
Willem
10/25/05
Read Re: On NP Completeness and Intractability
Ed Prochak
10/25/05
Read Re: On NP Completeness and Intractability
Dr. David Kirkby
10/25/05
Read Re: On NP Completeness and Intractability
Gene
10/25/05
Read Re: On NP Completeness and Intractability
MartDowd
10/25/05
Read Re: On NP Completeness and Intractability
RobertSzefler
10/25/05
Read Re: On NP Completeness and Intractability
Dr. David Kirkby
10/25/05
Read Re: On NP Completeness and Intractability
Pubkeybreaker
10/25/05
Read Re: On NP Completeness and Intractability
Wim Benthem
10/26/05
Read Re: On NP Completeness and Intractability
RobertSzefler
10/25/05
Read Re: On NP Completeness and Intractability
KP Bhat
10/25/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/25/05
Read Re: On NP Completeness and Intractability
tchow@lsa.umich.edu
10/25/05
Read Re: On NP Completeness and Intractability
googmeister@gmail.com
10/25/05
Read Re: On NP Completeness and Intractability
nimmi_srivastav@yahoo.com
10/25/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/26/05
Read Re: On NP Completeness and Intractability
tchow@lsa.umich.edu
10/27/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/25/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/25/05
Read Re: On NP Completeness and Intractability
Randy
10/25/05
Read Re: On NP Completeness and Intractability
C6L1V@shaw.ca
10/25/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/25/05
Read Re: On NP Completeness and Intractability
Wim Benthem
10/25/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/25/05
Read Re: On NP Completeness and Intractability
Randy
10/25/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/26/05
Read Re: On NP Completeness and Intractability
tchow@lsa.umich.edu
10/26/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
Arthur J. O'Dwyer
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
Willem
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/27/05
Read Re: On NP Completeness and Intractability
tchow@lsa.umich.edu
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
tchow@lsa.umich.edu
10/27/05
Read Re: On NP Completeness and Intractability
Joe Hendrix
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
Joe Hendrix
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/27/05
Read Re: On NP Completeness and Intractability
Arthur J. O'Dwyer
10/27/05
Read Re: On NP Completeness and Intractability
googmeister@gmail.com
10/27/05
Read Re: On NP Completeness and Intractability
tchow@lsa.umich.edu
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
Arthur J. O'Dwyer
10/28/05
Read Re: On NP Completeness and Intractability
Joe Hendrix
10/28/05
Read Re: On NP Completeness and Intractability
Ben Rudiak-Gould
10/28/05
Read Re: On NP Completeness and Intractability
Bryan Olson
10/28/05
Read Re: On NP Completeness and Intractability
Pekka Orponen
10/27/05
Read Re: On NP Completeness and Intractability
tchow@lsa.umich.edu
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/25/05
Read Re: On NP Completeness and Intractability
tchow@lsa.umich.edu
10/25/05
Read Re: On NP Completeness and Intractability
Michael J. Hennebry
10/25/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/25/05
Read Re: On NP Completeness and Intractability
Randy
10/25/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/25/05
Read Re: On NP Completeness and Intractability
Willem
10/25/05
Read Re: On NP Completeness and Intractability
Arthur J. O'Dwyer
10/25/05
Read Re: On NP Completeness and Intractability
googmeister@gmail.com
10/31/05
Read Re: On NP Completeness and Intractability
Oliver Wong
10/31/05
Read Re: On NP Completeness and Intractability
Robert Israel
11/1/05
Read Re: On NP Completeness and Intractability
Willem
11/1/05
Read Re: On NP Completeness and Intractability
googmeister@gmail.com
11/1/05
Read Re: On NP Completeness and Intractability
Willem
11/1/05
Read Re: On NP Completeness and Intractability
Torkel Franzen
11/1/05
Read Re: On NP Completeness and Intractability
googmeister@gmail.com
11/1/05
Read Re: On NP Completeness and Intractability
Oliver Wong
11/1/05
Read Re: On NP Completeness and Intractability
Willem
11/1/05
Read Re: On NP Completeness and Intractability
Robert Israel
10/26/05
Read Re: On NP Completeness and Intractability
Randy
10/26/05
Read Re: On NP Completeness and Intractability
stephen@nomail.com
10/26/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
Bryan Olson
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/27/05
Read Re: On NP Completeness and Intractability
Bryan Olson
10/27/05
Read Re: On NP Completeness and Intractability
Randy
10/25/05
Read Re: On NP Completeness and Intractability
Pat Farrell
10/25/05
Read On what "NP-Hard" means; was: Re: On NP Completeness and Intractability
Bryan Olson

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