The fusion of independently obtained stochastic maps by collaborating mobile agents is considered. The proposed approach includes two parts: matching of stochastic maps and maximum likelihood alignment. In particular, an affine invariant hypergraph is constructed for each stochastic map, and a bipartite matching via a linear program is used to establish landmark correspondence between stochastic maps. A maximum likelihood alignment procedure is proposed to determine rotation and translation between common landmarks in order to construct a global map within a common frame of reference. A main feature of the proposed approach is its scalability with respect to the number of landmarks: the matching step has polynomial complexity and the maximum likelihood alignment is obtained in closed form. Experimental validation of the proposed fusion approach is performed using the Victoria Park benchmark dataset.