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NP-COMPLETENESS All of the algorithms we have studied thus far have been polynomial-time algorithms: on inputs of size n, their worst-case running time is O(nk) for some constant k. It is natural to wonder whether all problems can be solved
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Algebraic number systems and boolean matrix multiplication

Algebraic number systems and boolean matrix multiplication The properties of matrix addition and multiplication depend on the properties of the underlying number system. In this section, we define three different kinds of underlying number syst
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String matching

STRING MATCHING Finding all occurrences of a pattern in a text is a problem that arises frequently in text-editing programs. Typically, the text is a document being edited, and the pattern searched for is a particular word supplied by the u
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Approximation algorithms

APPROXIMATION ALGORITHMS Many problems of practical significance are NP-complete but are too important to abandon merely because obtaining an optimal solution is intractable. If a problem is NP-complete, we are unlikely to find a polynomial
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