For some assembly structures, parallel disassembly of components is necessary in order to reach a particular internal component. Due to the large number of possible combinations, the parallel disassembly problem is not easily solved in a general form. In order to reduce the time complexity of finding a disassembly sequence, this paper introduces a simplified mating graph and develops a data structure to facilitate an efficient parallel disassembly algorithm. This algorithm takes Max {O(N3 ), O(E)} time to find an efficient sequence to reach a particular component, where N is the number of components and E is the number of mating faces. Separability testing is incorporated to determine whether the query component can be disassembled and moved to infinity without obstruction.