Consider an SQL query that involves joins of several relations, optionally followed by selections and/or projections. It can be represented by a conjunctive datalog query Q without negation or arithmetic subgoals. We consider the problem of answering such a query Q using a mediator M. For each relation R that corresponds to a subgoal in Q, M contains several sources; each source for R provides some of the tuples in R. The capability of each source are described in terms of templates. It might not be possible to get all the tuples in the result, Result(Q), using M, due to restrictions imposed by the templates. We consider best-effort query answering: Find as many tuples in Result(Q) as possible. We present an algorithm to determine if Q can be so answered using M. / Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science.