A problem is Np-Hard if all NP problems are reducible to an instance of that problem in polynomial time.
Some NP-Hard problems cannot be solved in nondeterministic polynomial time, and are not in NP.24 Oct 2018
Can NP complete problems be solved?
The main thing to take away from an NP-complete problem is that it cannot be solved in polynomial time in any known way. NP-Hard/NP-Complete is a way of showing that certain classes of problems are not solvable in realistic time.24 Nov 2008
Can NP hard problems be solved in polynomial time?
Consequences. If P ≠ NP, then NP-hard problems cannot be solved in polynomial time. Some NP-hard optimization problems can be polynomial-time approximated up to some constant approximation ratio (in particular, those in APX) or even up to any approximation ratio (those in PTAS or FPTAS).
What makes NP hard difficult?
NP-Hard Problem. A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.
Are NP hard problems in NP?
NP is the set of all problems whose solutions can be verified in polynomial time. NP-hard problems are informally defined as those that can’t be solved in polynomial time. In other words, the problems that are harder than P.9 Jun 2017