np-complete


Can it be proven no polynomial algorithm exists for an NP-Complete prob.?


I can't really seem to grasp what it really means to say a problem is NP-Complete. Could anyone help me with the following question?
An NP-complete problem is a problem for which one can prove that an algorithm for solving it in polynomial time does not exist. Is the statement true?
I would want to say this statement isn't true, because can anyone actually prove that such an algorithm doesn't exist for any NP-Complete problem? From looking around on various sources, I understand that no polynomial time algorithm is known for any NP-Complete problem; however, it can't be proven.
Any help would be greatly appreciated. Thanks.
It is possible in some situations to prove that no algorithm exists that is better than a certain limit.
For example the O(n log n) bound for a comparison sort has been proven. No matter how clever we become in the future, we can be sure that no-one will ever invent an O(n) comparison sort.
In this case though, no-one has found a proof. But that doesn't mean it can't be proven.
The statement is more fundamentally wrong: There are problems that cannot be solved in polynomial time which are much harder than NP problems. The point of NP completeness is a polynomial time solution existing is equivalent to P=NP (which means additionally that a solution not existing means P!=NP).

Related Links

Prove NP-Completeness of generating 2 shortest routes over given edge grouping constraints?
Reduction to Clique prob
Approximation Algorithm between two NP compete problems
Is it possible to find the probability to a solution of NP-complete problems?
Knapsack for each weight having multiple values - Is it possible to solve?
Reduction from Maximum independent set to Dominating set to prove the Dominating set is NP-complete
How I can prove that 2-CNF is not NP-complete?
When NP complete becomes NP hard
Can it be proven no polynomial algorithm exists for an NP-Complete prob.?
Effect of number base when proving NP completeness of numerical problems
How to reduce 3COLOR to 3SAT?
proof NP-complete
Proof that Dominating Set is NP-Complete
Is this an NP problem?
Given a collection of consumers competing for a limited resource, allocate that resource to maximize it's applicability
What is the difference between a 'combinatorial algorithm' and a 'linear algorithm'?

Categories

HOME
ibm-bluemix
log4j
listview
deezer
push-notification
google-api-php-client
electron
bpmn
webstorm
android-4.4-kitkat
survey
google-project-tango
ckeditor
opengl-es-2.0
append
numeral.js
handsontable
modx-revolution
collectd
circular-dependency
moonmail
netflix
django-simple-history
uitypeeditor
immutable.js
autocad-plugin
riot.js
physics-engine
arabic
realex-payments-api
claims-based-identity
lcd
sqlcipher
rst2pdf
buck
wtx
libssl
subdomains
c++-amp
procdump
iframe-resizer
ioio
usbserial
mpmediaquery
hexo
ios5
overlap
x11-forwarding
streamsets
xenforo
tasker
texmaker
powershell-dsc
http-live-streaming
nxlog
isbn
no-www
businessworks
python-webbrowser
dropbox-php
gabor-filter
nstextview
darcs
qtwebview
akka-cluster
epson
sonarlint-vs
query-performance
database-optimization
trash
skobbler-maps
gstreamer-0.10
disque
skype4py
whois
oauth2client
javax.sound.midi
separator
r-tree
reactive-banana
icu4j
ruby-2.2
tarjans-algorithm
emailrelay
ios9.1
mono-embedding
sailfish-os
system32
graph-api-explorer
e10s
umbraco6
npapi
sorl-thumbnail
html-helper
undefined-reference
didselectrowatindexpath
concurrent-collections
industrial
floating-point-precision
soundtouch
gwt-rpc
orchardcms-1.7
distutils
unc
nsnetservice
google-email-migration
twrequest
buildr
nsdatecomponents
inotifycollectionchanged
oncheckedchanged
site.master
sudzc
webkit.net
brewmp
kdbg
genealogy
mdac

Resources

Mobile Apps Dev
Database Users
javascript
java
csharp
php
android
MS Developer
developer works
python
ios
c
html
jquery
RDBMS discuss
Cloud Virtualization
Database Dev&Adm
javascript
java
csharp
php
python
android
jquery
ruby
ios
html
Mobile App
Mobile App
Mobile App