The problem of determining an optimal set of nodes to be accessed by a transaction in a partially replicated distributed database system can be formulated as a zero-one integer programming problem. Obtaining an optimal set of nodes is therefore an NP-hard problem. An O(n2) heuristic algorithm employing randomized decisions is developed for determining a near-optimal set of nodes. For small values of n, we can determine how close the heuristic solution is to the optimal set of nodes. We also compare our heuristic to other algorithms reported in the literature.