
Example of a problem that is NP-Hard but not NP-Complete
2017年5月22日 · This means that any complete problem for a class (e.g. PSPACE) which contains NP is also NP-hard. In order to get a problem which is NP-hard but not NP-complete, it suffices to find a computational class which (a) has complete problems, (b) provably contains NP, and (c) is provably different from NP. So:
algorithms - NP hard/complete - Mathematics Stack Exchange
The current hot topic has been the use of PCP Theorem to prove various NP-Hardness results for approximation versions of NP-Hard problems. So, non-determinism is still part of the definition of NP and is historically important, but the current status is that it is not mandatory.
What are NP-complete problems and why are they so important?
A problem in P is in NP by definition, but the converse may not be the case; probably the most important open question in computer science is whether classes P and NP are the same, that is P=NP. NP-complete is a family of NP problems for which you know that if one of them had a polynomial solution then everyone of them has.
optimization - Are there NP hard problems solved in P time ...
2019年9月2日 · A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it, and a problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP. If any NP-complete problem has a polynomial time algorithm, all problems in NP do.".
How do we know if a problem is hardest in NP
Such a problem is NP-hard and in NP. How do we know if a problem is hardest in NP, and no harder problem exists. I understand that let's assume that somehow magically we know that a problem L is hardest in NP and then we can find out more hardest problems H if we can reduce H to L and vice versa.But my question is how does it all begin?
definition - Difference between NP-hard and NP-complete
2016年6月15日 · NP-hard if all problems in NP polynomially reduce to it; and NP-complete if all problems in NP polynomially transform to it. What is the difference between polynomial reduction and polynomial transformation?
P and NP and NP-complete and NP-hard in simple terms
NP is the set of all problems that can be checked for correctness if you guess an answer. NP-hard is the set of all problems that are at least as hard as the hardest NP problems. NP-complete is the set of all problems are NP-hard problems that are also NP. Have I covered anything? Are there any important aspects that I still need to know?
Simple "real life" NP-hard problems? - Mathematics Stack Exchange
2011年5月17日 · I don't know if you would consider it "real life", but exact inference in Bayesian networks is NP-Hard; it's a straightforward reduction from 3-SAT (I guess one could argue that Bayesian inference is used in the playing of many games).
MILP: is it NP-complete or NP-hard?
2019年11月12日 · $\begingroup$ It might be good to add that while the decision variant of MILP lies in NP, the proof of this is not easy (at the least, proving MILP is NP-hard is a lot easier). Although an optimal point would work as a certificate, the tricky part is to show that we can always find an optimal point that can be encoded in polynomial size.
discrete mathematics - Why finding chromatic number is NP-Hard ...
2015年7月8日 · The problem 3-COLOURABILITY is NP-hard because there is a polynomial time reduction from 3-SAT to 3-COLOURABILITY and there is a reduction from SAT to 3-SAT. It is proven that if you can solve SAT in polynomial time, you can solve any NP problem in polynomial time (Cook's theorem).