Methods and apparatuses that search tree representations of a bitmap for available blocks to allocate in storage devices are described. An allocation request for a file may be received to initiate the search. In one embodiment, the bitmap may include an array of bits corresponding to blocks in the storage devices. Each bit may indicate whether one of the blocks is available. The tree representations may include at least one red-black tree having nodes corresponding to one or more consecutive bits in the bitmap indicating an extent of available blocks. One of the tree representations may be selected according to a file associated with an allocation request to identify an extent of available block matching the allocation request. The tree representations may be synchronized as the bitmap is updated with changes of block allocations in the storage devices.