Information om | Engelska ordet NP-COMPLETENESS

Exempel på hur man kan använda NP-COMPLETENESS i en mening

• The significance of NP-completeness was made clear by the publication in 1972 of Richard Karp's landmark paper, "Reducibility among combinatorial problems", in which he showed that 21 diverse combinatorial and graph theoretical problems, each infamous for its intractability, are NP-complete.
• Karp's reduction also implies the NP-completeness of the FVS problem on undirected graphs, where the problem stays NP-hard on graphs of maximum degree four.
• Blum and her co-authors, Michael Shub and Stephen Smale, showed that (analogously to the theory of Turing machines) one can define analogues of NP-completeness, undecidability, and universality for this model.
• Blum, Lenore, Mike Shub, and Steve Smale, (1989), "On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines", Bulletin of the American Mathematical Society, New Series, 21 (1): 1-46.
• This insight in turn indicates that NP-completeness is of parallel interest: computational intractability of a cosmos-consuming scale is a practical counterpart to traditional absolute uncomputability - another layer of impossibility for the idealizations.
• This problem appears as problem GT18 in Garey and Johnson's classical book on NP-completeness, and is a rather straightforward reformulation of.
• The NP-completeness of 3-dimensional matching is an example of one of Lawler's favorite observations, the "mystical power of twoness": for many combinatorial optimization problems that can be parametrized by an integer, the problem can be solved in polynomial time when the parameter is two but becomes NP-complete when the parameter is three.
• In 1982, Steve Mahaney published his proof that the nonexistence of sparse NP-complete languages (with NP-completeness defined in the standard way using many-one reductions) is in fact equivalent to the statement that P ≠ NP; this is Mahaney's theorem.
• Demaine, Löffler, and Schmidt (2021) further strengthened this by proving NP-completeness even if all galaxies are restricted to be rectangles of sizes 1×1, 1×3, or 3×1.

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