Abstract
This is the 25th edition of a column that covers new developments in the theory of NP-completeness. The presentation is modeled on that which M. R. Garey and I used in our book Computers and Intractability: A Guide to the Theory of NP-Completeness , W. H. Freeman & Co., New York, 1979, hereinafter referred to as “[G&J].” Previous columns, the first 23 of which appeared in Journal of Algorithms , will be referred to by a combination of their sequence number and year of appearance, for example, [Col 1, 1981]. Full bibliographic details on the previous columns as well as downloadable unofficial versions of them can be found at http://www.reseach.att.com/~dsj/columns/. This edition of the column discusses the wide range of lower bounds on approximation guarantees for NP-hard optimization problems both in their functional forms and in the hypotheses on which they depend.
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