exact algorithm 精确算法
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原文:
The phrase exact algorithm is used when talking about an algorithm that always finds the optimal solution to an optimization problem. (As opposed to heuristics that may sometimes produce worse solutions. A subset of these are the approximation algorithms – those are the ones where we can prove a guaranteed bound on the ratio between the optimal solution and the solution produced by the algorithm.)
For hard optimization problems (especially NP-hard ones) it is often the case that there are some polynomial-time approximation algorithms, but the best known exact algorithms require exponential time.
For example, there is a simple polynomial-time 2-approximation algorithm for Vertex Cover, but if you need an exact algorithm, the best one we know runs in, IIRC, O(1.1889 n ) . (Vertex Cover is also fixed-parameter tractable, but that’s a topic for another day.)
精确算法是指在最优化问题中,一个算法总是能找到最优解,(是相对于启发式算法来说的,启发式算法往往找到的不是最优解,启发式算法的一个子集是近似算法,近似算法的结果与最优解的比例有一个约束值,相当于误差范围,这个约束值是可以被证明的。)
NP hard问题往往有很多时间复杂度为多项式的近似算法,但是对应的精确算法的时间复杂度往往是指数级别的。
例如在定点覆盖问题中,有近似度为2的多项式复杂度近似算法,但是精确算法的时间复杂度为
原地址:http://www.quora.com/What-is-the-definition-of-exact-algorithm-in-Computer-Science
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