The database column already exists, just need to expose it. Should be an optional field that auto-generates a value if no value is given.
per @epriestley:
The alias would be a unique alphanumeric string like "restart", which could not contain special characters. It also could not be purely numeric (for example, you can't give a link the alias 123, because then U123 and the aliased link would both have the URL /u/123.
If a link has an alias, both /u/2 and /u/restart would still work correctly (adding an alias doesn't break old links). The detail URL is still /U2, and the edit URL is still /phurl/edit/2/ or whatever.