Two-dimensional packing algorithm can be used for allocating submeshes in mesh multiprocessor systems. Previously, we developed an efficient packing algorithm called TP heuristic, and showed how the results of the packing could be used for allocating submeshes. In this paper, we present theoretical performance bounds for TP heuristic. We also present a parallel version of the algorithm that consumes reduced time when it is executed by multiple processors in mesh multiprocessors.