Completeness in approximation classes
Information and Computation
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Mathematics of Operations Research
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Journal of the ACM (JACM)
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CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Completeness in approximation classes beyond APX
Theoretical Computer Science
Efficient approximation of min set cover by moderately exponential algorithms
Theoretical Computer Science
Approximation of min coloring by moderately exponential algorithms
Information Processing Letters
Survey: A survey on the structure of approximation classes
Computer Science Review
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ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Hi-index | 5.24 |
Several problems are known to be APX-, DAPX-, PTAS-, or Poly-APX-PB-complete under suitably defined approximation-preserving reductions. But, to our knowledge, no natural problem is known to be PTAS-complete and no problem at all is known to be Poly-APX-complete. On the other hand, DPTAS- and Poly-DAPX-completeness have not been studied until now. We first prove in this paper the existence of natural Poly-APX- and Poly-DAPX-complete problems under the well known PTAS-reduction and under the DPTAS-reduction (defined in "G. Ausiello, C. Bazgan, M. Demange, and V. Th. Paschos, Completeness in differential approximation classes, MFCS'03"), respectively. Next, we deal with PTAS- and DPTAS-completeness. We introduce approximation preserving reductions, called FT and DFT, respectively, and prove that, under these new reductions, natural problems are PTAS-complete, or DPTAS-complete. Then, we deal with the existence of intermediate problems under our reductions and we partially answer this question showing that the existence of NPO-intermediate problems under Turing-reductions is a sufficient condition for the existence of intermediate problems under both FT- and DFT-reductions. Finally, we show that MIN COLORING is DAPX-complete under DPTAS-reductions. This is the first DAPX-complete problem that is not simultaneously APX-complete.