Definition 4.2.1.6.Let U (I,So,L,LI,M,cost,goal)be an optimiza- tion problem.An algorithm A is called a polynomial-time approximation scheme (PTAS)for U,if;for every input pair (x,E)ELIXIR,A computes a feasible solution A(x)with a relative error at most e,and TimeA(,E1) can be bounded by a functions that is polynomial in.If TimeA(,e)can be bounded by a function that is polynomial in both and e1,then we say that A is a fully polynomial-time approximation scheme(FPTAS)for U. 问题：如何理解这句话： The advantage of PTASs is that the user has the choice of e in this tradeoff of the quality of the output and of the amount of computer work TimeA(x,1). 问题：在FPTAS定义中，时间复杂度界于ε1多项式是何用意？ 所以： Probably a FPTAS is the best that one can have for a NP-hard optimization problem
问题：在FPTAS定义中，时间复杂度界于ε -1多项式是何用意？ 问题：如何理解这句话： 所以：
问题：几个NPO的分类，其级别代表了什 么含义？ NPO(I): Contains every optimization problem from NPO for which there exists a FPTAS. In Section 4.3 we show that the knapsack problem belongs to this class. 有“最好的”近似算法方案的NPO问题
问题：几个NPO的分类，其级别代表了什 么含义？ 有“最好的” 近似算法方案的NPO问题