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Overview: The practical and theoretical relevance of problems to the NP-complete degree vf complexity are widely known. From the practical point of view it is sufficient to remember that in this class we find most of the combinatorial and optimization problems which b,,.·e the widest range of applications, for example scheduling problems, optimization problems on graphs, integer programming etc. As far as the theoretical relevance is concerned ;;.•e should remember that one of the most outstanding problems in Computer Science, the problem of deciding whether any NP-complete set can be recognized in polynomial time, coincides with the problem of knowing whether the computation power of a nondeterministic Turing machine which accepts a set in polynomial time is strictly stronger than the power of ordinary polynomially bounded Turing machines or not. Until recen#y the design of algorithms for finding exact approximate solutions to practical instances of hard combinatorial and optimization problems was the main concern of experts in Operations Research while the study of the complexity of these problems with respect to various computation models and the analysis of general solution techniques was the main interest of computer scientists.
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