Abstract
The inapproximability of non NP-hard optimization problems is investigated. Based on self-reducibility and approximation preserving reductions, it is shown that problems Log Dominating Set, Tournament Dominating Set and Rich Hypergraph Vertex Cover cannot be approximated to a constant ratio in polynomial time unless the corresponding NP-hard versions are also approximable in deterministic subexponential time. A direct connection is established between non NP-hard problems and a PCP characterization of NP. Reductions from the PCP characterization show that Log Clique is not approximable in polynomial time and Max Sparse SAT does not have a PTAS under the assumption that SAT cannot be solved in deterministic \( 2^{O(log n \sqrt n )} \)time and that NP \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \not\subset } \) DTIME\( (2^{O(n)} ) \).
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Cai, L., Juedes, D., Kanj, I. (1998). The Inapproximability of Non NP-hard Optimization Problems. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_46
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