Completeness in approximation classes beyond APX
نویسندگان
چکیده
منابع مشابه
Completeness in approximation classes beyond APX
We present a reduction that allows us to establish completeness results for several approximation classes mainly beyond APX. Using it, we extend one of the basic results of S. Khanna, R. Motwani, M. Sudan, and U. Vazirani (On syntactic versus computational views of approximability, SIAM J. Comput., 28:164–191, 1998) by proving the existence of complete problems for the whole Log-APX, the class ...
متن کاملCompleteness in standard and differential approximation classes: Poly-(D)APX- and (D)PTAS-completeness
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, DPTASand Poly-DAPX-completeness have not been studied until now. We first prove in this paper the existence of nat...
متن کاملPoly-APX- and PTAS-Completeness in Standard and Differential Approximation
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 standar...
متن کاملCompleteness in Differential Approximation Classes
We study completeness in differential approximability classes. In differential approximation, the quality of an approximation algorithm is the measure of both how far is the solution computed from a worst one and how close is it to an optimal one. The main classes considered are DAPX, the differential counterpart of APX, including the NP optimization problems approximable in polynomial time wit...
متن کاملComplexity Classes and Completeness in Algebraic Geometry
We study the computational complexity of sequences of projective varieties. We define analogues of the complexity classes P and NP for these and prove the NP-completeness of a sequence called the universal circuit resultant. This is the first family of compact spaces shown to be NP-complete in a geometric setting. Valiant's theory of algebraic/arithmetic complexity classes is an algebraic analo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2006
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2006.05.023