Approximation Complexity of Max-Cut on Power Law Graphs

In this paper we study the MAX-CUT problem on power law graphs (PLGs) with power law exponent β. We prove some new approximability results on that problem. In particular we show that there exist polynomial time approximation schemes (PTAS) for MAX-CUT on PLGs for the power law exponent β in the interval (0, 2). For β > 2 we show that for some ε > 0, MAX-CUT is NP-hard to approximate within approximation ratio 1 + ε, ruling out the existence of a PTAS in this case. Moreover we give an approximation algorithm with improved constant approximation ratio for the case of β > 2.