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Random self-reducibility : ウィキペディア英語版
Random self-reducibility
Random self-reducibility (RSR) is the rule that a good algorithm for the average case implies a good algorithm for the worst case. RSR is the ability to solve all instances of a problem by solving a large fraction of the instances.
==Definition==
If a function ''f'' evaluating any instance ''x'' can be reduced in polynomial time to the evaluation of ''f'' on one or more random instances ''yi'', then it is self-reducible (this is also known as a ''non-adaptive uniform self-reduction''). In a random self-reduction, an arbitrary worst-case instance ''x'' in the domain of ''f'' is mapped to a random set of instances ''y''1, ..., ''yk''. This is done so that ''f''(''x'') can be computed in polynomial time, given the coin-toss sequence from the mapping, ''x'', and ''f''(''y''1), ..., ''f''(''yk''). Therefore, taking the average with respect to the induced distribution on ''yi'', the average-case complexity of ''f'' is the same (within polynomial factors) as the worst-case randomized complexity of ''f''.
One special case of note is when each random instance ''yi'' is distributed uniformly over the entire set of elements in the domain of ''f'' that have a length of |''x''|. In this case ''f'' is as hard on average as it is in the worst case. This approach contains two key restrictions. First the generation of ''y''1, ..., ''yk'' is performed non-adaptively. This means that ''y''2 is picked before ''f''(''y''1) is known. Second, it is not necessary that the points ''y''1, ..., ''yk'' be uniformly distributed.

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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