Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
tchow@lsa.umich.edu

Posts: 1,133
Registered: 12/6/04
Re: On NP Completeness and Intractability
Posted: Oct 25, 2005 6:30 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <1130277999.884543.197050@g43g2000cwa.googlegroups.com>,
KP Bhat <kbhat@sta.samsung.com> wrote:
>The meaning of the word "hard" refers to time complexity. In order to
>be NP-Hard, the time complexity should be worse than or equal to the
>time complexity of a known problem in NP.


Even if "known problem in NP" is amended to "known NP-complete problem,"
this is inaccurate, and it's a common misconception, so it's worth
clearing up. A problem is NP-hard if every problem in NP reduces to
it ("reduce" here typically means polytime Karp reduction, but slight
variants on this definition are also seen sometimes in the literature).

There are NP-complete problems that are solvable in time c^n for some
constant c. It does not follow that, for example, a problem that is
complete for DTIME(c^(2n)) is necessarily NP-hard. Just because the
time complexity is greater doesn't automatically mean that there is
a reduction.

This point is important because part of the reason that the P = NP
conjecture is difficult is that we don't really understand well the
relationship between nondeterminism and time complexity. One can prove
the bounds P <= NP <= EXP but essentially nothing more precise is known.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences


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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.