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We consider the problem of generating a large state-space in a distributed fashion. Unlike previously proposed solutions that partition the set of reachable states according to a hashing function provided by the user, we explore heuristic methods that completely automate the process. The first step is an initial random walk through the state space to initialize a search tree, duplicated in each processor. Then, the reachability graph is built in a distributed way, using the search tree to assign each newly found state to classes assigned to the available processors. Furthermore, we explore two remapping criteria that attempt to balance memory usage or future workload, respectively. We show how the cost of computing the global snapshot required for remapping will scale up for system sizes in the foreseeable future. An extensive set of results is presented to support our conclusions that remapping is extremely beneficial.