An allocator for a reduction processor which evaluates programs stored as binary graphs employing variable-free applicative language codes. These graphs are made up of nodes, each of which exists in memory and contains as its most significant bit a mark bit which when set indicates that the node is being used in a graph and when reset indicates that the node or storage location is available for future use by the processor. The allocator scans selected groups of storage locations in parallel to see if there are any unused storage locations and then places the addresses of those unused storage locations in a queue for use by the processor.