A computer being able to estimate the geometry of a room could benefit applications such as auralization, robot navigation, virtual reality and teleconferencing. When estimating the geometry of a room using multiple microphones, the main challenge is to identify which reflections, or echoes, originate from the same wall and can, therefore, be modeled by a virtual source outside the room using the mirror image source model. In this paper we present a new and efficient method to disambiguate the echoes using a graph theoretical approach where echo combinations are modeled as nodes in a graph and the problem is stated as a maximum independent set problem. Once the echoes are correctly labelled, we know the locations of the virtual sources from which we can infer the room geometry. Experiments for shoe-box shaped rooms show that we can reliably estimate the room geometry within seconds on contemporary hardware and achieve centimeter precision on finding the vertices of the room.@en