NP-hard problems

NP-hard problem in combinatorial optimization

assignment of colors to elements of a graph subject to certain constraints

alt=Euler diagram for P, NP, NP-complete, and NP-hard set of problems.|thumb|300px|Euler diagram for P, NP, NP-complete, and NP-hard set of problems. The left side is valid under the assumption that P≠NP, while the right side is valid under the assumption that P=NP (except that the empty language and its complement are never NP-complete). In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a solution for H takes 1 unit

combinatorial optimization problem