We use variants of the generalized CNF satisfiability problems SAT(S) of T.J. Schhaefer (1978) to characterize the efficient approximability of a number of basic NP and PSPACE-hard optimization problems in the literature. In contrast with the recent results, none of our proofs make use of interactive proof systems or of probabilistically checkable debate systems. In particular assuming P/spl ne/NP- or P/spl ne/PSPACE, we show that a number of the optimization problems shown not to be efficiently approximable can be shown not to be efficiently approximable by direct reductions, often of variants of the problems MAX NSF and ambiguous 3SAT. Moreover, often we show this, not only for arbitrary problem instances but also for planar problem instances and for f(n)-treewidth-bounded instances. Thus analogous to Zuckerman (1993), we show that: "Planar NP-complete, PSPACE-complete, planar PSPACE-complete problems, etc. also have versions that are hard to approximate".
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机译:我们使用T.J.的广义CNF可满足性问题SAT(S)的变体。 Schhaefer(1978)在文献中描述了许多基本的NP和PSPACE硬优化问题的有效逼近性。与最近的结果相反,我们的证据均未使用交互式证据系统或概率可检查的辩论系统。特别是,假设P / spl ne / NP-或P / spl ne / PSPACE,我们表明,通过直接归纳(通常是Ps的变体),许多显示为不能有效逼近的优化问题就不能显示为有效逼近。 MAX NSF和模棱两可的3SAT问题。此外,我们经常显示这一点,不仅针对任意问题实例,而且针对平面问题实例以及f(n)-树宽限制实例。因此类似于Zuckerman(1993),我们证明:“平面NP-完全,PSPACE-完全,平面PSPACE-完全问题等也具有难以近似的版本”。
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