A large class of computational problems involve the determination of properties of graphs, digraphs, integers, arrays of integers, finite families of finite sets, boolean formulas and elements of other countable domains. Through simple encodings from such domains into the set of words over a finite alphabet these problems can be converted into language recognition problems, and we can inquire into their computational complexity. It is reasonable to consider such a problem satisfactorily solved when an algorithm for its solution is found which terminates within a number of steps bounded by a polynomial in the length of the input. We show that a large number of classic unsolved problems of covering, matching, packing, routing, assignment and sequencing are equivalent, in the sense that either each of them possesses a polynomial-bounded algorithm or none of them does.
85-103
false
Reducibility among Combinatorial Problems
1972-01-01
chapters
2019-04-15T20:47
en
1972
http://link.springer.com/10.1007/978-1-4684-2001-2_9
https://scigraph.springernature.com/explorer/license/
chapter
Jean D.
Bohlinger
readcube_id
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978-1-4684-2003-6
978-1-4684-2001-2
Complexity of Computer Computations
Springer Nature - SN SciGraph project
Richard M.
Karp
Raymond E.
Miller
10.1007/978-1-4684-2001-2_9
doi
Computation Theory and Mathematics
Boston, MA
Springer US
Information and Computing Sciences
Thatcher
James W.
University of California, Berkeley
University of California, Berkeley, USA
dimensions_id
pub.1007977430