算法概论——课后习题8.3

问题

STINGY SAT is the following problem: given a set of clauses (each a disjunction of literals) and

an integer k, and a satisfying assignment in which at most k variables are true, if such an

assignment exists. Prove that STINGY SAT is NP-complete.

证明

证明STINGY SAT是一个NPC问题，只需要2步：

1. STINGY SAT是一个NP问题：STINGY SAT问题的解可以在多项式时间内验证。
2. 可以将SAT问题归约到STINGY SAT问题：将k设成SAT问题中变量的个数。

综上，STINGY SAT是一个NPC问题。