Methods, systems, and apparatus, including computer programs encoded on computer storage media, for executing concurrent writes to a data store. One of the systems includes a data store comprising a plurality of storage segments, wherein each storage segment comprises a plurality of blocks; and an allocator system comprising: a plurality of threads, and a plurality of bitmaps each corresponding to a respective storage segment of the data store, wherein the allocator system is configured to perform operations comprising: assigning a respective bitmap to each thread of the plurality of threads; and executing, by each thread of the plurality of threads, one or more write requests to one or more blocks of the storage segment corresponding to the thread using the bitmap assigned to the thread, wherein executing a write request by a thread includes updating the bitmap assigned to the thread.