Other Complexity Classes and Measures Chapter 29 of the forthcoming CRC Handbook on Algorithms and Theory of Computation
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چکیده
Some natural problems seem not to be complete for any of the complexity classes we have seen so far. For example, consider the problem of taking as input a graph G and a number k, and deciding whether k is exactly the length of the shortest traveling salesperson’s tour. This is clearly related to the TSP problem discussed in Chapter 28, Section 3, but in contrast to TSP, it seems not to belong to NP, and also seems not to belong to co-NP. To classify and understand this and other problems, we will introduce a few more complexity classes. We cannot discuss all of the classes that have been studied—there are further pointers to the literature at the end of this chapter. Our goal is to describe some of the most important classes, such as those defined by probabilistic and interactive computation. Supported by the National Science Foundation under Grant CCR-9509603. Portions of this work were performed while a visiting scholar at the Institute of Mathematical Sciences, Madras, India. Supported by the National Science Foundation under Grant CCR-9315696. Supported by the National Science Foundation under Grant CCR-9409104.
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Other Complexity Classes and Measures
Some natural problems seem not to be complete for any of the complexity classes we have seen so far. For example, consider the problem of taking as input a graph G and a number k, and deciding whether k is exactly the length of the shortest traveling salesperson’s tour. This is clearly related to the problem discussed in Chapter 28, Section 3, but in contrast to , it seems not to belong to NP, ...
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