Subset sum problem

Decision problem in computer science

The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . The problem is known to be NP-complete. Moreover, some restricted variants of it are NP-complete too, for example:The variant 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.

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