The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions...
**NP-Completeness: ** if all NP problem "Y" can be reduced to an NP problem "X", "X" is NP-Complete. Suppose X is NP-Complete, X is solvable in polynomial time, if and only if "P = NP". **How to establish NP-completeness of problem "Y". **: step1: Show that "Y" is...
Techniques for best-case, worst-case and average-case time and space analysis. Designing algorithms using induction, divide-and-conquer and greedy strategies. Algorithms: sorting and order statistics, trees, graphs, matrices. Intractability: classes P, NP, and NP-completeness, approximation algorithms...
NP-Completeness(CNF-SAT, cli) A decision problem P is NP-Complete if two conditions are satisfies:(1) It is NP; (2) Every other problem P' in NP is polynomially reducible to P.
到这为止NP-hardness和NP-completeness就很好理解了。称问题L是NP-hard,如果任意一个NP的问题都可以...
P指求解该问题需要 "Polynomial time", NP指验证一个回答是该问题的答案是"Non-deterministic Polynomial...
Biconditional (BC): P IFF Q. Therefore, (P IMPLIES Q) AND (Q IMPLIES P) 还有一些Derived Rules: De Morgan's Law (德摩根定律) NOT(A\ \ AND \ \ B) \iff NOT(A)\ \ OR \ \ NOT(B) NOT(A\ \ OR \ \ B) \iff NOT(A)\ \ AND \ \ NOT(B) ...
几乎所有没有已知多项式算法的NP问题,即几乎所有看似困难的容易验证的问题都具有相同的性质,这被称为NP完全问题(NP-completeness)。这意味着所有NP完全问题(包括哈密顿路径问题、数独和其他成千上万的问题)在精确意义上是等价的。"你面对的这些所有不同的问题,都神奇地变成了同一个问题,但我们仍不知道它是否能被...
几乎所有没有已知多项式算法的NP问题,即几乎所有看似困难的容易验证的问题都具有相同的性质,这被称为NP完全问题(NP-completeness)。这意味着所有NP完全问题(包括哈密顿路径问题、数独和其他成千上万的问题)在精确意义上是等价的。“你面对的这些所有不同的问题,都神奇地变成了同一个问题,但我们仍不知道它是否能被...
P与NP关系:P问题是NP问题的子集,也就是说,所有P问题都是NP问题。这是因为如果一个问题可以在多项式...