NP-Complete
A class of problems in computational complexity theory that belongs to the class NP and to which every problem in NP can be reduced in polynomial time. Such problems typically require exponential search or heuristic approximation to solve.
Timeline (last 90 days)
P2NPCBench is a new benchmark comprising 12 question families, each consisting of an NP-complete problem and a polynomial-time solvable problem with identical surface wording.
NP-complete problems are the hardest class within NP, and any NP problem can be reduced to them in polynomial time; classic examples include the decision version of the traveling salesman problem, the Boolean satisfiability problem (SAT), and the 3-coloring problem for graphs.
Even for graph classes that are recognizable in polynomial time, their corresponding sandwich problems may be NP-complete.
The Cook-Levin theorem proves that the SAT problem is NP-complete.
All Facts (4)
P2NPCBench is a new benchmark comprising 12 question families, each consisting of an NP-complete problem and a polynomial-time solvable problem with identical surface wording.
50%UnverifiedNP-complete problems are the hardest class within NP, and any NP problem can be reduced to them in polynomial time; classic examples include the decision version of the traveling salesman problem, the Boolean satisfiability problem (SAT), and the 3-coloring problem for graphs.
50%UnverifiedEven for graph classes that are recognizable in polynomial time, their corresponding sandwich problems may be NP-complete.
50%UnverifiedThe Cook-Levin theorem proves that the SAT problem is NP-complete.
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