Completeness in approximation classes
Information and Computation
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximate solution of NP optimization problems
Theoretical Computer Science
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
Approximating discrete collections via local improvements
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
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We first prove the existence of natural Poly-APX-complete problems, for both standard and differential approximation paradigms, under already defined and studied suitable approximation preserving reductions Next, we devise new approximation preserving reductions, called FT and DFT, respectively, and prove that, under these reductions, natural problems are PTAS-complete, always for both standard and differential approximation paradigms To our knowledge, no natural problem was known to be PTAS-complete and no problem was known to be Poly-APX-complete until now We also deal with the existence of intermediate problems under FT- and DFT-reductions and we show that such problems exist provided that there exist NPO-intermediate problems under Turing-reduction Finally, we show that min coloring is APX-complete for the differential approximation.