0

I have a general question, I know there is a way to find 2-approximation for maximization problems by finding 2 solution s1 and s2 s.t

q(s1)+q(s2)>=q(OPT)

and by chosing max{q(s1),q(s2)} i've found a legit approx.

Back to my question, Is it possible to do this general method for minimization problems ? What will be the analog?

limitless
  • 669
  • 7
  • 18
  • 1
    That does not make much sense to me (in the general-case). Would you add some context please? As edge-coloring can be formulated as maximization-problem and it's not APX-complete, there is no such constant-factor approximation. Doesn't that contradict your initial statement? – sascha Feb 24 '17 at 20:36
  • for example, You can find 2-approx for the Knapsack problem when you sort by the Specific value and if k is the last item that by picking him youll overflow the knapsack, you can choose between the 1,2,...,k-1 items or the k item as a final answer and you'll get 2-approx – limitless Feb 24 '17 at 20:40
  • **But that's not general**. It's limited to this specific problem! – sascha Feb 24 '17 at 20:40
  • It isnt specific for maximization problems – limitless Feb 24 '17 at 20:40
  • But why, isnt the max value of two soultions that there sum is bigger than the optimal soultion will raise at least half of opt ? – limitless Feb 24 '17 at 20:43
  • @sascha Ok you are right, if i'll change it to general in a sense that the optinal solution is a number, that will be correct ? – limitless Feb 24 '17 at 20:48
  • 1
    I still don't know what you want to express here. It's way to informal and i'm afraid that won't change that fast. Nonetheless, [this probably answers your question](http://cs.stackexchange.com/questions/48776/converting-maximization-to-minimization-in-aproximation-algorithms). – sascha Feb 24 '17 at 20:52
  • Thanks, That is what i meant – limitless Feb 24 '17 at 20:54

0 Answers0