Allocation performance is enhanced by optimizing queries associated with the allocation. A sparse definition space for a calculation is translated into a dense space for performing the calculation for efficient resource utilization. A calculation expression is symbolically analyzed to determine a relationship between non-zero calculated results and non-zero cells in the input data. From this relationship the regions on which the calculated results are non-zero are obtained by examining the input data. The calculation space is thus reduced to a smaller one. The resulting calculation space is no longer sparse and enables efficient performance of allocation.