This paper proposes the lookahead idea in job allocation in a mesh-connected parallel processor, which has become popular in the design of massively parallel computers. The allocation heuristic can select its strategy by lookahead, i.e., looking into the queue of waiting jobs. This approach is shown to be superior to the existing heuristics which do not utilize and lookahead. For efficient implementation, we propose a compact rectangular set representation of the free submesh area which allows the complete submesh detection (also allocation) algorithm(s) to be an order of magnitude improved (in the average case) over the existing approach(es). The proposed representation is also beneficial when considering some currently unexplored issues in processor allocation and practitioner's approach.