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...
8 KB (1,082 words) - 09:57, 24 July 2024
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...
4 KB (642 words) - 19:47, 7 May 2023
Longest path problem (category NP-complete problems)
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...
22 KB (2,662 words) - 01:59, 2 January 2024
Pseudo-polynomial time (section Strong and weak NP-hardness vs. strong and weak polynomial-time algorithms)
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...
5 KB (876 words) - 07:57, 4 December 2023
Optimal facility location (section NP hardness)
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...
21 KB (3,147 words) - 06:53, 22 July 2024
TFNP (section F(NP ∩ coNP))
are no known unconditional intractability results or results showing NP-hardness of TFNP problems. TFNP is not believed to have any complete problems...
17 KB (2,698 words) - 03:24, 30 April 2024
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...
29 KB (2,746 words) - 06:55, 5 September 2024
computational hardness assumption such as P ≠ NP. Computer scientists have different ways of assessing which hardness assumptions are more reliable. We say that...
27 KB (3,227 words) - 22:38, 20 December 2023
to P versus NP problem. Fortnow, L.; Gasarch, W. "Computational complexity". Aviad Rubinstein's Hardness of Approximation Between P and NP, winner of the...
63 KB (7,784 words) - 23:34, 5 September 2024
Feedback vertex set (category NP-complete problems)
computational hardness assumption, it is NP-hard to approximate the problem to within any constant factor in polynomial time. The same hardness result was...
16 KB (1,781 words) - 21:22, 20 August 2024