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In 1967, [[Manuel Blum]] formulated a set of [[axiom]]s (now known as [[Blum axioms]]) specifying desirable properties of complexity measures on the set of computable functions and proved an important result, the so-called [[Blum's speedup theorem|speed-up theorem]]. The field began to flourish in 1971 when the [[Stephen Cook]] and [[Leonid Levin]] [[Cook–Levin theorem|proved]] the existence of practically relevant problems that are [[NP-complete]]. In 1972, [[Richard Karp]] took this idea a leap forward with his landmark paper, "Reducibility Among Combinatorial Problems", in which he showed that 21 diverse [[combinatorics|combinatorial]] and [[graph theory|graph theoretical]] problems, each infamous for its computational intractability, are NP-complete.<ref>{{Citation | author = Richard M. Karp | chapter = Reducibility Among Combinatorial Problems | chapter-url = http://www.cs.berkeley.edu/~luca/cs172/karp.pdf | title = Complexity of Computer Computations |editor= R. E. Miller |editor2=J. W. Thatcher| publisher = New York: Plenum | pages = 85–103 | year = 1972}}</ref>

In 1967, [[Manuel Blum]] formulated a set of [[axiom]]s (now known as [[Blum axioms]]) specifying desirable properties of complexity measures on the set of computable functions and proved an important result, the so-called [[Blum's speedup theorem|speed-up theorem]]. The field began to flourish in 1971 when the [[Stephen Cook]] and [[Leonid Levin]] [[Cook–Levin theorem|proved]] the existence of practically relevant problems that are [[NP-complete]]. In 1972, [[Richard Karp]] took this idea a leap forward with his landmark paper, "Reducibility Among Combinatorial Problems", in which he showed that 21 diverse [[combinatorics|combinatorial]] and [[graph theory|graph theoretical]] problems, each infamous for its computational intractability, are NP-complete.<ref>{{Citation | author = Richard M. Karp | chapter = Reducibility Among Combinatorial Problems | chapter-url = http://www.cs.berkeley.edu/~luca/cs172/karp.pdf | title = Complexity of Computer Computations |editor= R. E. Miller |editor2=J. W. Thatcher| publisher = New York: Plenum | pages = 85–103 | year = 1972}}</ref>

1967年，[[Manuel Blum]]提出了一组[[公理]]s（现在称为[[Blum axioms]]），规定了可计算函数集合上复杂性测度的理想性质，并证明了一个重要结果，即所谓的[[Blum加速定理|加速定理]]。这个领域在1971年开始蓬勃发展，当时[[Stephen Cook]]和[[Leonid Levin]][[Cook–Levin定理|证明了[[NP complete]]实际相关问题的存在。1972年，[[Richard Karp]]以其里程碑式的论文《组合问题中的可还原性》（Reductibility In Combinational Problems）将这一想法向前推进了一大步，在这篇论文中，他展示了21个不同的[[组合学|组合]]和[[图论|图论]]问题，每一个都因其计算难处理而臭名昭著，是NP完全的。<ref>{引文{author=Richard M.Karp | chapter=组合问题之间的可约性|章url=http://www.cs.berkeley.edu/~luca/cs172/karp.pdf|title=计算机计算的复杂性

1967年，[[Manuel Blum]]提出了一组[[公理]]s（现在称为[[Blum axioms]]），规定了可计算函数集合上复杂性测度的理想性质，并证明了一个重要结果，即所谓的[[Blum加速定理|加速定理]]。这个领域在1971年开始蓬勃发展，当时[[Stephen Cook]]和[[Leonid Levin]][[Cook–Levin定理|证明了[[NP complete]]实际相关问题的存在。1972年，[[Richard Karp]]以其里程碑式的论文《组合问题中的可还原性》（Reductibility In Combinational Problems）将这一想法向前推进了一大步，在这篇论文中，他展示了21个不同的[[组合学|组合]]和[[图论|图论]]问题，每一个都因其计算难处理而声名狼藉，是NP完全的。<ref>{{Citation | author = Richard M. Karp | chapter = Reducibility Among Combinatorial Problems | chapter-url = http://www.cs.berkeley.edu/~luca/cs172/karp.pdf | title = Complexity of Computer Computations |editor= R. E. Miller |editor2=J. W. Thatcher| publisher = New York: Plenum | pages = 85–103 | year = 1972}}</ref>

In the 1980s, much work was done on the average difficulty of solving NP-complete problems—both exactly and approximately. At that time, computational complexity theory was at its height, and it was widely believed that if a problem turned out to be NP-complete, then there was little chance of being able to work with the problem in a practical situation. However, it became increasingly clear that this is not always the case{{cn|reason=passive, no source|date=August 2019}}, and some authors claimed that general asymptotic results are often unimportant for typical problems arising in practice.<ref>{{cite book|last=Wolfram|first=Stephen|title=A New Kind of Science|publisher=Wolfram Media, Inc.|year=2002|page=[https://archive.org/details/newkindofscience00wolf/page/1143 1143]|isbn=978-1-57955-008-0|url-access=registration|url=https://archive.org/details/newkindofscience00wolf/page/1143}}</ref>

In the 1980s, much work was done on the average difficulty of solving NP-complete problems—both exactly and approximately. At that time, computational complexity theory was at its height, and it was widely believed that if a problem turned out to be NP-complete, then there was little chance of being able to work with the problem in a practical situation. However, it became increasingly clear that this is not always the case{{cn|reason=passive, no source|date=August 2019}}, and some authors claimed that general asymptotic results are often unimportant for typical problems arising in practice.<ref>{{cite book|last=Wolfram|first=Stephen|title=A New Kind of Science|publisher=Wolfram Media, Inc.|year=2002|page=[https://archive.org/details/newkindofscience00wolf/page/1143 1143]|isbn=978-1-57955-008-0|url-access=registration|url=https://archive.org/details/newkindofscience00wolf/page/1143}}</ref>