Completeness in approximation classes beyong APX (septembre 2005)

Bruno Escoffier (1) , Vangelis Th. Paschos (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

We present a reduction that allows us to establish completeness results for several ap- proximation 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 of problems approximable within ra- tios that are logarithms of the size of the instance. We also introduce a new approximability class, called Poly-APX(Δ), dealing with graph-problems approximable with ratios func- tions of the maximum degree Δ of the input graph. For this class also, using the reduction propose, we establish complete problems.

Bruno Escoffier, Vangelis Th. Paschos. Completeness in approximation classes beyong APX (septembre 2005). 2005. ⟨hal-00013651⟩