A library manager to determine a relay-point library string when a particular cartridge (specific cartridge) is moved to an empty drive (target drive) for mounting. A method for determining a relay-point library string includes: receiving a command to mount a cartridge in a library string located on one side of the relay-point library string; searching for the target drive among library strings, and finding the target drive in a library string on the other side of an interposed relay-point library string relative to the library string in which the specific cartridge is located; selecting a relay-point library string based on predetermined conditions to move the specific cartridge using shuttle connections to the found target drive; and searching to determine whether or there is a newly available drive in a relay-point library string other than the selected relay-point library string before the selected cartridge reaches the selected relay-point library string.