You can store the values in a trie (e.g., with one node per character in the string). Exact lookup in the trie is O(string_length), like a hash table. Inexact lookup can similarly walk the tree, but explore side branches within a certain budget.

So if your string is "abc", you'd follow the node for "a", then the one for "b", but _also_ the one for "c", at a cost of 1 (because dropping the "b" incurs an edit distance of 1).