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Karp's 21 NP-complete problems — Richard Karp

1972 AD · Transmission: Global
MathematicsTheoryNorth American

Richard Karp, at the University of California, Berkeley, published in 1972 "Reducibility Among Combinatorial Problems", taking Stephen Cook's 1971 result — which establishes the existence of NP-complete problems via the case of Boolean satisfiability — and showing that twenty-one other classic combinatorial problems, appearing completely different from one another, are also NP-complete: the traveling salesman problem (finding the shortest route visiting a set of cities exactly once), graph coloring, the knapsack problem, the maximum independent set problem, and many others. The technique Karp employs — reducing one problem to another via transformations that preserve computational difficulty — becomes the standard method for classifying new problems as NP-complete without needing to prove their difficulty directly from scratch: it suffices to show that a known problem can be translated into the new problem in polynomial time. The article transforms NP-completeness from an isolated theoretical curiosity into a structural property found throughout practical computer science: thousands of optimization problems in logistics, scheduling, network design, and computational biology turn out to be NP-complete, which explains why approximate or heuristic algorithms are used in practice instead of seeking guaranteed exact solutions.

InstitutionUniversity of California, Berkeley
Historical regionUSA
Primary sourceKarp, R.M. — "Reducibility Among Combinatorial Problems" in Complexity of Computer Computations (Plenum Press, 85–103, 1972). DOI: 10.1007/978-1-4684-2001-2_9
Secondary sourceTuring Award 1985 — Press release (amturing.acm.org)
Original languageEnglish
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