as hard as NP, but not necessarily in NP. NP-equivalent Decision problems that are both NP-hard and NP-easy, but not necessarily in NP. NP-intermediate...

by the input size. Thus strong NP-completeness or NP-hardness may also be defined as the NP-completeness or NP-hardness of this unary version of the problem...

solved by a pseudo-polynomial time algorithm unless P = NP. The strong/weak kinds of NP-hardness are defined analogously. Consider the problem of testing...

cannot be solved in polynomial time for arbitrary graphs unless P = NP. Stronger hardness results are also known showing that it is difficult to approximate...

costs of the facilities. The facility location problem on general graphs is NP-hard to solve optimally, by reduction from (for example) the set cover problem...

are no known unconditional intractability results or results showing NP-hardness of TFNP problems. TFNP is not believed to have any complete problems...

computational hardness assumption such as P ≠ NP. Computer scientists have different ways of assessing which hardness assumptions are more reliable. We say that...

Cormode, Graham (2004). The hardness of the lemmings game, or Oh no, more NP-completeness proofs (PDF). Light Up is NP-Complete Friedman, Erich (27 March...

computational hardness assumption, it is NP-hard to approximate the problem to within any constant factor in polynomial time. The same hardness result was...

problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input agents in binary coding. If a problem is strongly NP-hard, then it...

to P versus NP problem. Fortnow, L.; Gasarch, W. "Computational complexity". Aviad Rubinstein's Hardness of Approximation Between P and NP, winner of the...

vertex cover to integer programming that will serve as the proof of NP-hardness. Let G = ( V , E ) {\displaystyle G=(V,E)} be an undirected graph. Define...

of its hardness proof, unless P = NP, it has no polynomial time approximation ratio better than 1.3606. This is the same threshold for hardness of approximation...

average of the pairwise distances; both are NP-hard. Finding a minimum weight weakly fundamental basis is also NP-hard, and approximating it is MAXSNP-hard...

results about the hardness of approximation algorithms to be proven. All problems in P, denoted P ⊆ N P {\displaystyle {\mathsf {P\subseteq NP}}} . Given a...

unique games conjecture is often used in hardness of approximation. The conjecture postulates the NP-hardness of the following promise problem known as...

Since the traveling salesman problem is NP-hard, the job-shop problem with sequence-dependent setup is clearly also NP-hard since the TSP is a special case...

Koroth, Mertz and Pitassi (2020) to NP-hardness of automating Cutting Planes; and by Garlík (2020) to NP-hardness of automating k-DNF Resolution. It is...

(e.g., they may be used to generate good seed values). Results about NP-hardness in theoretical computer science make heuristics the only viable option...

problem becomes NP-hard, implying that finding a polynomial time approximation for the problem is impossible unless NP=P. Some hardness of approximation...

with up to 4,177 entities and 20,531 features. As expected, due to the NP-hardness of the subjacent optimization problem, the computational time of optimal...

should be used. Explicit proofs of NP-hardness are given in later papers: Yu, Hoogeveen and Lenstra prove NP-hardness of a very restricted version of Numerical...

(2^{\operatorname {poly} (\log n)})} . Dinur et al. strengthened this by giving a NP-hardness result with ϵ = ( log ⁡ log ⁡ n ) c {\displaystyle \epsilon =(\log \log...

satisfiability problem and the quantified boolean formula problem. Because of its NP-hardness, large-size MAX-SAT instances cannot in general be solved exactly, and...

problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems...

polynomial time. Thus Circuit SAT belongs to complexity class NP. To show NP-hardness, it is possible to construct a reduction from 3SAT to Circuit SAT...

we construct a 4-set in A, with sum T. The NP-hardness of 3-partition was used to prove the NP-hardness rectangle packing, as well as of Tetris and some...

Selection. Complexity theory List of films about mathematicians NP-hardness P-hardness Regan, K. W. "The Travelling Salesman's Power". Retrieved April...

ordering exists, and whether a Hamiltonian path exists, despite the NP-hardness of the Hamiltonian path problem for more general directed graphs (i.e...

same sum). This problem is strongly NP-hard. Kovalyov and Pesch discuss a generic approach to proving NP-hardness of partition-type problems. One application...