<p><b>Abstract</b>—We introduce a new two-phase technique to solve highly asymmetric assignment problems. In the first phase, the assignment problem is decomposed into subproblems which are solved in parallel. The first phase is used to exclude certain suboptimal assignments from consideration in the second phase. In the second phase, the optimal assignment is finalized. We show that the two-phase algorithm can reduce the theoretical time bound for solving an <tmath>$n \times k$</tmath> assignment problem (<tmath>$n < k$</tmath>) by a factor of <tmath>$\sqrt{\frac{k}{n}}$</tmath>.</p>