INFR 11102 : Computational Complexity 06 / 02 / 2018 Lecture 7 : More on NP - completeness
نویسنده
چکیده
After Cook’s paper [Coo71] published, Dick Karp immediately realized that the notion of NP-hardness captures a large amount of intractable combinatorial optimization problems. In [Kar72], he showed 21 problems to be NP-complete. This list quickly increased and by the time of 1979, Garey and Johnson [GJ79] wrote a whole book on NP-complete problems. This book has became a classic nowadays, and thousands of NP-hard problems were discovered during the past four decades. These intractable problems spread over all kinds of areas, even beyond computer science. The canonical hard problem LNP defined last time is not very useful to show NP-hardness of other problems, and Sat is much more handier in this sense. What is even more useful is the following variant of Sat. Let k-CNF formulas be those whose clauses involve at most k literals. For example, (x1 ∨ x2 ∨ x3 ∨ x4) ∧ (x2 ∨ x5) is a 4-CNF.
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