in which all inputs are positive.
* The variant in which inputs may be positive or negative, and . For example, given the set , the answer is yes because the subset sums to zero.
* The variant in which all inputs are positive, and the target sum is exactly half the sum of all inputs, i.e., . This special case of SSP is known as the partition problem.

SSP can also be regarded as an optimization problem: find a subset whose sum is at most