In this article we describe and compare several recently proposed algorithms for precise submesh allocation in a two-dimensional mesh connected system. The methods surveyed include various frame sliding strategies, the maximum boundary value heuristic, and interval set scan techniques. In addition, a new enhancement to the interval set scan method is described. This enhancement results in an algorithm that has better allocation and run-time performance under a FCFS scheduling policy than any of the other proposed methods. We present results drawn from an extensive simulation study to illustrate the relative efficiency of the various methods.