Relational Algebra – Grouping with Multiple Attributes

DISCLAIMER : Never Learned Relational Algebra but it looks interesting

From the schema given and your question, this is what the SQL should be:

SELECT
    emp_mgr.person_name
FROM
    manages emp_mgr
    INNER JOIN employee emp ON emp_mgr.person_name  = emp.person_name
    INNER JOIN employee mgr ON emp_mgr.manager_name = mgr.person_name
WHERE
    emp.street = mgr.street AND
    emp.city = mgr.city
;

Here is another query that only uses JOINs, no WHERE clause:

SELECT
    emp.person_name
FROM
    (SELECT A.person_name,B.street,B.city FROM manages A
    INNER JOIN employee B ON A.person_name = B.person_name) emp
    NATURAL JOIN
    (SELECT A.manager_name,B.street,B.city FROM manages A
    INNER JOIN employee B ON A.manager_name = B.person_name) mgr
;

The first query gets all employees who are managed and their managers in the form of a Cartesian Product. Then, it looks for a common street and city.

The second query collects personnel records (name,street,city) of employees and their managers and performs a NATURAL JOIN between the employess and their managers using (street,city).

If you can transalate both queries back to Relational Algebra, I think you will have what you are looking for. I believe the second may be of better help.

Yes, but.

If an entity only has one attribute, then that attribute must serve as an identifier for the entity. Typically, if only one attribute is found for an entity in the given data stream, then another attribute is "invented" for purposes of identifying. It's often called "id", it's often an integer, and it's often populated using the autonumber feature of the database system.

When you are doing analysis, it's important to distinguish between the features that were given to you in the problem statement, and the features you added in order to make sense out of the problem.