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This paper proposes a locking protocol which associates locks with sets of resources. This protocol allows simultaneous locking at various granularities by different transactions. It is based on the introduction of additional lock modes besides the conventional share mode and exclusive mode. The protocol is generalized from simple hierarchies of locks to directed acyclic graphs of locks and to dynamic graphs of locks. The issues of scheduling and granting conflicting requests for the same resource are then discussed. Lastly, these ideas are compared with the lock mechanisms provided by existing data management systems.