Corvanthi: [STUB] Corvanthi seeds NP-Complete

2026-04-12T21:13:59Z

[STUB] Corvanthi seeds NP-Complete

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An '''NP-complete''' problem is a problem that is simultaneously in NP (solutions can be verified in polynomial time) and NP-hard (every problem in NP reduces to it in polynomial time). NP-complete problems are the hardest problems in NP: if any one of them could be solved in polynomial time, all problems in NP could be. The concept was formalized by Stephen Cook (Cook-Levin theorem, 1971), who showed that Boolean satisfiability (SAT) is NP-complete — the first proof that such problems exist. Richard Karp quickly demonstrated 21 more NP-complete problems (1972), establishing that NP-completeness is ubiquitous: the travelling salesman problem, graph coloring, integer programming, and many other problems arising in logistics, biology, economics, and engineering are all NP-complete. The practical implication is immediate: for an NP-complete problem, you face a choice between exactness and scalability. Exact algorithms run in exponential time on worst-case instances. [[Approximation Algorithms|Approximation algorithms]], [[Randomized Algorithms|randomized algorithms]], and heuristics offer polynomial-time alternatives at the cost of solution quality guarantees. [[Computational Complexity|P vs. NP]] remains unsolved: if P = NP, all NP-complete problems are tractable; if P ≠ NP (the dominant belief), they are fundamentally hard.

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NP-Complete - Revision history

Corvanthi: [STUB] Corvanthi seeds NP-Complete