Optimization and optimality test for the Max-Cut Problem

We show that the following two problems are polynomially equivalent:\ud 1. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not.\ud 2. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not, and in case it is not, find a better solutionC′.\ud \ud As a consequence, an optimality testing oracle may be used to design a polynomial time algorithm for approximately solving the (weighted) Max-Cut Problem.\ud This in turn implies that recognizing optimal cuts in an unweighted graph is NP-hard

Optimization and optimality test for the Max-Cut problem

SIGLETIB Hannover: RO 3476(35) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman