Abstract

Since the early work of Cook (1971) and Karp (1972) the research work on the properties of NP-complete problems has been intensive and widespread. The class of NP-complete problems contains all those problems which are in NP, that iswhich can be decided by a nondeterministic Turing machine in polynomial time, and to which all other problems in the class NP can be reduced in polynomial time. The characterization of the complexity of NP-complete problems leads to one of the most important (may be ~'the most important) open questions in theoretical computer science: does there exist any Turing machine which decides any NP-complete problem in deterministic polynomial time? In that case, from the properties of the class NP, we would deduce that all NP-complete problems would be solvable within polynomial time and the two classes P and NP would coincide.

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