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The algorithm for wildcard searching in SQL involves using special characters like "%" and "_" to match one or more characters in a search pattern. Here is a general outline of how the algorithm works:

1. Choose the column(s) to search in and construct a search pattern with wildcard characters.
2. Use the "LIKE" operator to filter the results based on the search pattern.
3. Use "%" to match zero or more characters of any type in the search pattern.
4. Use "_" to match any single character in the search pattern.
5. Use square brackets [ ] to match any one character in a range or a set of characters.

For example, if you want to search for all names that start with "J" and end with "n" but have any number of characters in between, you can use the following query:

SELECT * FROM customers WHERE name LIKE 'J%n';

This will return all records in the "customers" table where the "name" column starts with "J" and ends with "n" with any number of characters in between.