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- W2000611521 abstract "The field of computational complexity for concrete, practical combinatorial problems has developed in a remarkably smooth fashion. One can point to several features of the theory of polynomial-time computability which make it especially well-behaved, including: (1) the modelling of feasible computing by polynomial-time complexity is well-supported by the fact that almost all known polynomial-time algorithms for natural problems have running times bounded by polynomials of small degree; (2) problems are invariably known to be decidable in polynomial time by direct evidence in the form of efficient algorithms; (3) while the theory is formulated in terms of decision problems, almost all known algorithms proceed by actually constructing a solution to the problem at hand. Herein we illustrate how recent advances in graph theory and graph algorithms dramatically alter this situation on all three counts. Powerful and easy-to-apply tools are now available for classifying problems as decidable in polynomial time by nonconstructively proving only the existence of polynomial-time decision algorithms. These tools neither specify the degree of the polynomial, nor produce the decision algorithm, nor guarantee that such an algorithm is of any use in constructing a solution. These developments present both practitioners and theories with novel challenges." @default.
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- W2000611521 date "1987-11-01" @default.
- W2000611521 modified "2023-09-28" @default.
- W2000611521 title "Nonconstructive advances in polynomial-time complexity" @default.
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- W2000611521 doi "https://doi.org/10.1016/0020-0190(87)90054-8" @default.
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