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L-reduction : ウィキペディア英語版
L-reduction
In computer science, particularly the study of approximation algorithms, an
L-reduction ("''linear reduction''") is a transformation of optimization problems which linearly preserves approximability features; it is one type of approximation-preserving reduction. L-reductions in studies of approximability of optimization problems play a similar role to that of polynomial reductions in the studies of computational complexity of decision problems.
The term ''L reduction'' is sometimes used to refer to log-space reductions, by analogy with the complexity class L, but this is a different concept.
==Definition==
Let A and B be optimization problems and cA and cB their respective cost functions. A pair of functions ''f'' and ''g'' is an L-reduction if all of the following conditions are met:
* functions ''f'' and ''g'' are computable in polynomial time,
* if ''x'' is an instance of problem A, then ''f''(''x'') is an instance of problem B,
* if ''y' '' is a solution to ''f''(''x''), then ''g''(''y' '') is a solution to ''x'',
* there exists a positive constant α such that
:\mathrm(f(x)) \le \alpha \mathrm(x),
* there exists a positive constant β such that for every solution ''y' '' to ''f''(''x'')
:|\mathrm(x)-c_A(g(y'))| \le \beta |\mathrm(f(x))-c_B(y')|.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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