算法概论 8.3题

Problem:
STINGY SAT is the following problem : given a set of clauses (each a disjunction of literals) and an integer k , find a satisfying assignment in which at most k variables are true , if such an assignment exists. Prove that STINGY SAT is NP-complete .

解答：STINGY SAT 的解是可以在多项式时间内验证其正确性的，要证明STINGY SAT是NP-complete的，只要找出方法把SAT规约为STINGY SAT即可。由题意可以看出SAT跟STINGY SAT是很像的，只要把SAT中变量的个数限制为k，就得到了STINGY SAT问题。由此可知STINGY SAT为NP-complete。