# Subset Summation Decision Task

A Subset Sum Problem is a computational decision task that is a summation task on a subset of a non-empty integer set.

**See:**Computational Complexity Theory, Cryptography, NP-Complete, Knapsack Problem, Partition Problem.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/subset_sum_problem Retrieved:2014-3-3.
- In computer science, the
**subset sum problem**is an important problem in complexity theory and cryptography. The problem is this: given a set of integers, is there a non-empty subset whose sum is zero? For example, given the set {−7, −3, −2, 5, 8}, the answer is*yes*because the subset {−3, −2, 5} sums to zero. The problem is NP-complete.An equivalent problem is this: given a set of integers and an integer

*s*, does any non-empty subset sum to*s*? Subset sum can also be thought of as a special case of the knapsack problem.^{[1]}One interesting special case of subset sum is the partition problem, in which*s*is half of the sum of all elements in the set.

- In computer science, the

- ↑ Martello, Silvano; Toth, Paolo (1990). "4 Subset-sum problem".
*Knapsack problems: Algorithms and computer interpretations*. Wiley-Interscience. pp. 105–136. ISBN 0-471-92420-2. MR1086874.