np-complete


Approximation Algorithm between two NP compete problems


Suppose that a O(n2)-time alpha-approximate algorithm exists for one of the two problems in each of the following pairs:
Vertex Cover and Independent Set
Independent Set and Clique
Max-Flow and Min-Cut
Does this guarantee that a O(n2)-time alpha-approximate algorithm exists for the other problem in the pair? I know that Clique reduces to Independent Set which in turn reduces to Vertex Cover.
Not necessarily, for two reasons.
First of all, NP reductions are generally not linear in complexity. Some of them are, but usually a problem of complexity n will reduce to some other NP problem of size n^3 or something. Even if we found a linear-time 3SAT algorithm, we wouldn't have found linear-time algorithms for all NP-hard problems -- just polynomial algorithms. So if by "similar" you mean "also n^2", not in general.
Secondly, approximations don't generally transfer. Because of the non-linear growth in complexity (that's a simplification of why, but it'll do), approximation guarantees generally don't survive the reduction process. As a result, while all NP-complete problems are in a sense comrades in exact solution hardness, they are far from it in approximation hardness.
In certain specific cases, approximations do transfer (and one of your examples -- left as an exercise for the reader -- most definitely transfers). But it's in no way guaranteed.

Related Links

Grid dominating set is NP-complete
Given a graph with n vertices and m edges, does it contain a simple cycle of length ⌈n/2⌉?
NP-complete or NP-hard?
Why using linear integer programming (ILP) though it is NP-Complete?
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

Categories

HOME
wso2
comparison
octobercms
rsync
yahoo-oauth
elm
malloc
jgroups
c#-2.0
onelogin
webrequest
contact
slick-slider
session-variables
commonmark
caml
fatal-error
pugjs
visual-composer
swiftlint
reverse-proxy
visjs
clickonce
errorlevel
web-sql
trading
android-widget
qhull
url-scheme
pingfederate
applozic
sql-server-2012-express
yadcf
preg-match-all
titanium-mobile
commit
repo
hexo
gesture
sqlite2
elasticsearch-plugin
unoconv
firebase-admin
nand2tetris
heightmap
import-from-excel
logfiles
dotcover
domain-model
mu
mplayer
capacity
imanage
eventkit
abcpdf9
deadbolt-2
probability-density
log4c
intrusion-detection
multi-level
mikroc
natvis
prerequisites
thredds
jmeter-maven-plugin
tmuxinator
coveralls
tarjans-algorithm
sortedlist
composite
notify
truevault
umbraco6
python-green
issuu
html-helper
onactivityresult
reactfx
didselectrowatindexpath
resty-gwt
app42
typo3-neos
page-layout
oam
ruby-datamapper
bulkloader
batterylevel
chronoforms
limejs
ocunit
android-hardware
clipper
angularjs-controller
typoscript2
chuck
bitsharp
isnullorempty
coderush
regsvr32
bubble-chart
nsobject
qt-jambi
hirefire
joyent
tomcat-valve
remember-me
paster
infrastructure
database-management
compiler-specific
brewmp
memory-size
temporal-database
anti-piracy
spec#
defensive-programming
zune
geneva-server

Resources

Database Users
RDBMS discuss
Database Dev&Adm
javascript
java
csharp
php
android
javascript
java
csharp
php
python
android
jquery
ruby
ios
html
Mobile App
Mobile App
Mobile App