Approximation Algorithm for the Max-Cut Problem

In this project, we investigated several approximation algorithms for the Max-Cut problem. Our main approach to this problem is a semideenite program (GW) based algorithm that has a performance guarantee of at least 0.878 of the optimal cut. We also show that we can perform exhaustive local search on top of the GW to enhance the result. Our results show that the running time of the local search is eecient compared to the time needed for GW, and the local search can almost always produce better result. We also investigated other heuristics to solve the Max-Cut problem: Metropolis, Simulated Annealing and local search without GW. We show that Metropolis, Simulated Annealing, and GW plus local search are eeective for Max-Cut when the number of nodes in the graph is less than 100. When the graph grows, our results show that Simulated Annealing is the most eeective in terms of quality, time and converging time.