With what Frequency are Apparently Intractable Problems Difficult?
Name
MIT-LCS-TM-126.pdf
Size
2.38 MB
Format
Adobe PDF
Checksum (MD5)
e43ccfa3f33e3fe350365e9210b80641
Author(s)
Meyer, A.R.
Paterson, M.S.
Date Issued
February 1979
Series/Report no.
MIT-LCS-TM-126
Abstract
An algorithm is almost polynomial-time (apt) iff there is a polynomial p such that for all n, the algorithm halts within p(n) steps on all by at most p(n) inputs of size at most n. It is nown that for NP-complete and polynomial space-complete problems, as well as certain other apparently intractable problems such as integer factoring, the following conditions are equivalent: (1) the problem is solveable by an apt algorithm, (2) the problem (or its complement) is polynomial-time transformable to a polynomial-sparse set, (3) the problem is solvable in polynomial time.
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